BIG_DATA_BFS_Segunda_Parte_con_preguntas_ipynb.ipynb

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        "<a href=\"https://colab.research.google.com/github/sgevatschnaider/Grafos/blob/main/BIG_DATA_BFS_Segunda_Parte_con_preguntas_ipynb.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML actualizado\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Material Elaborado por Sergio Gevatschnaider</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: Arial, sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1 {\n",
        "            color: #333;\n",
        "            text-align: center;\n",
        "            font-size: 2.5em;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        h2 {\n",
        "            color: #0066cc;\n",
        "            font-size: 2em;\n",
        "            margin-top: 20px;\n",
        "        }\n",
        "        h3 {\n",
        "            color: #333;\n",
        "            font-size: 1.5em;\n",
        "            margin-top: 15px;\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        a {\n",
        "            color: #0066cc;\n",
        "            text-decoration: none;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        a:hover {\n",
        "            text-decoration: underline;\n",
        "        }\n",
        "        .download-link {\n",
        "            background-color: #0066cc;\n",
        "            color: white;\n",
        "            padding: 10px 15px;\n",
        "            text-align: center;\n",
        "            display: inline-block;\n",
        "            border-radius: 5px;\n",
        "            margin-top: 20px;\n",
        "        }\n",
        "        .download-link:hover {\n",
        "            background-color: #004999;\n",
        "        }\n",
        "        .nested-ul {\n",
        "            list-style-type: disc;\n",
        "            margin-left: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Material Elaborado por Sergio Gevatschnaider</h1>\n",
        "    <p>Clase de Big Data de la Universidad de Palermo</p>\n",
        "    <p>Basado en el libro <em>Introduction to Graph Theory: A Short Course in Graph Theory</em> por Jacques Verstraete</p>\n",
        "    <p>El libro se puede descargar en este enlace:</p>\n",
        "    <p><a href=\"https://cseweb.ucsd.edu/~dakane/Math154/154-textbook.pdf\" target=\"_blank\" class=\"download-link\">Descargar libro</a></p>\n",
        "\n",
        "    <h2>Índice del Colab</h2>\n",
        "    <ul>\n",
        "        <li>Proposición 3.1.3: Todo Grafo Conexo Contiene un Árbol Generador</li>\n",
        "        <li>Definición de árbol generador</li>\n",
        "        <li>Método para encontrar un árbol generador</li>\n",
        "        <li>Eliminación de ciclos en un grafo</li>\n",
        "        <li>Algoritmo de Búsqueda en Anchura (BFS)\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Definición y pasos del algoritmo BFS</li>\n",
        "                <li>Selección de un vértice inicial</li>\n",
        "                <li>Construcción del árbol por niveles</li>\n",
        "                <li>Verificación de conectividad</li>\n",
        "                <li>Añadir aristas al árbol</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li>Ejemplo del Diámetro y Radio de un Grafo\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Definición de diámetro</li>\n",
        "                <li>Definición de radio</li>\n",
        "                <li>Cálculo de ambas propiedades en un grafo conexo</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li>Complejidad del Algoritmo BFS\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Tiempo de ejecución: O(V(G) + E(G))</li>\n",
        "                <li>Factores que afectan la complejidad</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li>Resumen\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Proposición 3.1.3</li>\n",
        "                <li>Uso del BFS para construir un árbol generador</li>\n",
        "                <li>Verificación de bipartición</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li>Árbol de Búsqueda en Anchura (BFS)\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Ejemplo: Construcción de un árbol de BFS</li>\n",
        "                <li>Organización de niveles en el árbol</li>\n",
        "                <li>Ejemplos de exploración de vértices</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li>Árbol Generador en el Grafo de Petersen\n",
        "            <ul class=\"nested-ul\">\n",
        "                <li>Descripción del grafo de Petersen</li>\n",
        "                <li>Aplicación del algoritmo BFS en el grafo</li>\n",
        "                <li>Exploración de vecinos y construcción del árbol generador</li>\n",
        "                <li>Organización en niveles</li>\n",
        "                <li>Propiedades del grafo (diámetro, radio)</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "    </ul>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML actualizado en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "Ptx0tbVk8k70",
        "outputId": "1e0c2c59-c11e-4139-810b-de94cd93ee78"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Material Elaborado por Sergio Gevatschnaider</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: Arial, sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1 {\n",
              "            color: #333;\n",
              "            text-align: center;\n",
              "            font-size: 2.5em;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        h2 {\n",
              "            color: #0066cc;\n",
              "            font-size: 2em;\n",
              "            margin-top: 20px;\n",
              "        }\n",
              "        h3 {\n",
              "            color: #333;\n",
              "            font-size: 1.5em;\n",
              "            margin-top: 15px;\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        a {\n",
              "            color: #0066cc;\n",
              "            text-decoration: none;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "        a:hover {\n",
              "            text-decoration: underline;\n",
              "        }\n",
              "        .download-link {\n",
              "            background-color: #0066cc;\n",
              "            color: white;\n",
              "            padding: 10px 15px;\n",
              "            text-align: center;\n",
              "            display: inline-block;\n",
              "            border-radius: 5px;\n",
              "            margin-top: 20px;\n",
              "        }\n",
              "        .download-link:hover {\n",
              "            background-color: #004999;\n",
              "        }\n",
              "        .nested-ul {\n",
              "            list-style-type: disc;\n",
              "            margin-left: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Material Elaborado por Sergio Gevatschnaider</h1>\n",
              "    <p>Clase de Big Data de la Universidad de Palermo</p>\n",
              "    <p>Basado en el libro <em>Introduction to Graph Theory: A Short Course in Graph Theory</em> por Jacques Verstraete</p>\n",
              "    <p>El libro se puede descargar en este enlace:</p>\n",
              "    <p><a href=\"https://cseweb.ucsd.edu/~dakane/Math154/154-textbook.pdf\" target=\"_blank\" class=\"download-link\">Descargar libro</a></p>\n",
              "\n",
              "    <h2>Índice del Colab</h2>\n",
              "    <ul>\n",
              "        <li>Proposición 3.1.3: Todo Grafo Conexo Contiene un Árbol Generador</li>\n",
              "        <li>Definición de árbol generador</li>\n",
              "        <li>Método para encontrar un árbol generador</li>\n",
              "        <li>Eliminación de ciclos en un grafo</li>\n",
              "        <li>Algoritmo de Búsqueda en Anchura (BFS)\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Definición y pasos del algoritmo BFS</li>\n",
              "                <li>Selección de un vértice inicial</li>\n",
              "                <li>Construcción del árbol por niveles</li>\n",
              "                <li>Verificación de conectividad</li>\n",
              "                <li>Añadir aristas al árbol</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li>Ejemplo del Diámetro y Radio de un Grafo\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Definición de diámetro</li>\n",
              "                <li>Definición de radio</li>\n",
              "                <li>Cálculo de ambas propiedades en un grafo conexo</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li>Complejidad del Algoritmo BFS\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Tiempo de ejecución: O(V(G) + E(G))</li>\n",
              "                <li>Factores que afectan la complejidad</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li>Resumen\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Proposición 3.1.3</li>\n",
              "                <li>Uso del BFS para construir un árbol generador</li>\n",
              "                <li>Verificación de bipartición</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li>Árbol de Búsqueda en Anchura (BFS)\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Ejemplo: Construcción de un árbol de BFS</li>\n",
              "                <li>Organización de niveles en el árbol</li>\n",
              "                <li>Ejemplos de exploración de vértices</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li>Árbol Generador en el Grafo de Petersen\n",
              "            <ul class=\"nested-ul\">\n",
              "                <li>Descripción del grafo de Petersen</li>\n",
              "                <li>Aplicación del algoritmo BFS en el grafo</li>\n",
              "                <li>Exploración de vecinos y construcción del árbol generador</li>\n",
              "                <li>Organización en niveles</li>\n",
              "                <li>Propiedades del grafo (diámetro, radio)</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "    </ul>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "bkDIMOZz9Tlr",
        "outputId": "d5900f89-8d85-4822-a922-3b2b13e97db1"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Proposición 3.1.3: Árbol Generador</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: Arial, sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2E8B57;\n",
              "            margin-top: 20px;\n",
              "        }\n",
              "        h1 {\n",
              "            font-size: 2.5em;\n",
              "            text-align: center;\n",
              "        }\n",
              "        h2 {\n",
              "            font-size: 1.8em;\n",
              "        }\n",
              "        h3 {\n",
              "            font-size: 1.5em;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: disc;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        code {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 2px 4px;\n",
              "            font-family: Consolas, \"Courier New\", monospace;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1em;\n",
              "            overflow-x: auto;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "\n",
              "    <h1>Proposición 3.1.3: Todo grafo conexo contiene un árbol generador</h1>\n",
              "\n",
              "    <p>Esta proposición establece que todo grafo <strong>conexo</strong> contiene al menos un <strong>árbol generador</strong> (<em>spanning tree</em>). Es decir, a partir de cualquier grafo conexo (donde cualquier par de vértices está conectado por un camino), es posible encontrar un subgrafo que conecte todos los vértices sin ciclos.</p>\n",
              "\n",
              "    <h2>Demostración</h2>\n",
              "    <p>La prueba proporciona una forma sencilla de encontrar un árbol generador. El método consiste en lo siguiente:</p>\n",
              "    <ul>\n",
              "        <li><strong>Buscar ciclos</strong> en el grafo.</li>\n",
              "        <li><strong>Eliminar</strong> una arista de cada ciclo encontrado.</li>\n",
              "        <li><strong>Repetir</strong> el proceso hasta que no queden ciclos, lo que garantiza que el grafo resultante es acíclico y sigue siendo conexo, formando así un árbol generador.</li>\n",
              "    </ul>\n",
              "\n",
              "    <h2>Algoritmo de Búsqueda en Anchura (Breadth-First Search, BFS)</h2>\n",
              "    <p>Una forma algorítmica de encontrar un árbol generador, directamente relacionada con la búsqueda de ciclos, es mediante el <strong>algoritmo de búsqueda en anchura (BFS)</strong>. Este algoritmo no solo permite encontrar un árbol generador, sino también verificar si un grafo es <strong>bipartito</strong> (divisible en dos conjuntos de vértices, A y B, donde no hay aristas entre vértices del mismo conjunto).</p>\n",
              "\n",
              "    <h3>Pasos del Algoritmo BFS para Encontrar un Árbol Generador</h3>\n",
              "    <ol>\n",
              "        <li><strong>Seleccionar un vértice inicial</strong> <code>v<sub>0</sub></code>: Elegimos cualquier vértice <code>v<sub>0</sub></code> del grafo <code>G</code> como la raíz del árbol generador.</li>\n",
              "        <li><strong>Construcción del árbol por niveles</strong>: \n",
              "            <ul>\n",
              "                <li>Colocamos <code>v<sub>0</sub></code> en el nivel 0 del árbol.</li>\n",
              "                <li>Identificamos todos los vértices vecinos de <code>v<sub>0</sub></code> (distancia 1), y los agregamos al siguiente nivel del árbol.</li>\n",
              "                <li>Repetimos el proceso con los vecinos de los vecinos, añadiendo vértices a niveles sucesivos según su distancia mínima a <code>v<sub>0</sub></code>.</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li><strong>Verificación de conectividad</strong>: Si el conjunto de vértices en el árbol es igual al conjunto total de vértices de <code>G</code>, entonces hemos completado el árbol generador.</li>\n",
              "        <li><strong>Añadir aristas</strong>: En cada paso, se elige un vértice <code>v<sub>i</sub></code> que ya está en el árbol y se agrega una arista hacia su vecino <code>w</code> que aún no está en el árbol.</li>\n",
              "    </ol>\n",
              "\n",
              "    <h2>Ejemplo del Diámetro y Radio de un Grafo</h2>\n",
              "    <p>El <strong>diámetro</strong> de un grafo es la máxima distancia entre dos vértices en un grafo conexo. Si el camino más largo entre dos vértices tiene una longitud de 4, entonces el diámetro es 4.</p>\n",
              "\n",
              "    <p>El <strong>radio</strong> de un grafo es la mínima distancia <code>r</code> tal que todos los vértices están como máximo a una distancia <code>r</code> de algún vértice central. En un grafo con radio 2, todos los vértices están a lo sumo a una distancia de 2 de un vértice particular.</p>\n",
              "\n",
              "    <h2>Complejidad del Algoritmo</h2>\n",
              "    <p>El tiempo de ejecución del algoritmo BFS es <code>O(V(G) + E(G))</code>, donde:</p>\n",
              "    <ul>\n",
              "        <li><code>V(G)</code>: Es el número de vértices en el grafo.</li>\n",
              "        <li><code>E(G)</code>: Es el número de aristas.</li>\n",
              "    </ul>\n",
              "    <p>Esto se debe a que cada vértice se visita una vez, y cada arista se explora una vez para asegurar que todos los vértices se hayan conectado.</p>\n",
              "\n",
              "    <h2>Resumen</h2>\n",
              "    <ul>\n",
              "        <li><strong>Proposición 3.1.3:</strong> Todo grafo conexo contiene un árbol generador.</li>\n",
              "        <li><strong>Búsqueda en Anchura (BFS):</strong> Un algoritmo eficiente para construir un árbol generador y verificar la bipartición de un grafo.</li>\n",
              "        <li>El algoritmo funciona explorando los vecinos de un vértice inicial en orden de cercanía (distancia), agregando vértices al árbol a medida que se avanza.</li>\n",
              "    </ul>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "from IPython.core.display import display, HTML\n",
        "\n",
        "# Contenido HTML para la Proposición 3.1.3 y BFS\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Proposición 3.1.3: Árbol Generador</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: Arial, sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2E8B57;\n",
        "            margin-top: 20px;\n",
        "        }\n",
        "        h1 {\n",
        "            font-size: 2.5em;\n",
        "            text-align: center;\n",
        "        }\n",
        "        h2 {\n",
        "            font-size: 1.8em;\n",
        "        }\n",
        "        h3 {\n",
        "            font-size: 1.5em;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: disc;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        code {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 2px 4px;\n",
        "            font-family: Consolas, \"Courier New\", monospace;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1em;\n",
        "            overflow-x: auto;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "\n",
        "    <h1>Proposición 3.1.3: Todo grafo conexo contiene un árbol generador</h1>\n",
        "\n",
        "    <p>Esta proposición establece que todo grafo <strong>conexo</strong> contiene al menos un <strong>árbol generador</strong> (<em>spanning tree</em>). Es decir, a partir de cualquier grafo conexo (donde cualquier par de vértices está conectado por un camino), es posible encontrar un subgrafo que conecte todos los vértices sin ciclos.</p>\n",
        "\n",
        "    <h2>Demostración</h2>\n",
        "    <p>La prueba proporciona una forma sencilla de encontrar un árbol generador. El método consiste en lo siguiente:</p>\n",
        "    <ul>\n",
        "        <li><strong>Buscar ciclos</strong> en el grafo.</li>\n",
        "        <li><strong>Eliminar</strong> una arista de cada ciclo encontrado.</li>\n",
        "        <li><strong>Repetir</strong> el proceso hasta que no queden ciclos, lo que garantiza que el grafo resultante es acíclico y sigue siendo conexo, formando así un árbol generador.</li>\n",
        "    </ul>\n",
        "\n",
        "    <h2>Algoritmo de Búsqueda en Anchura (Breadth-First Search, BFS)</h2>\n",
        "    <p>Una forma algorítmica de encontrar un árbol generador, directamente relacionada con la búsqueda de ciclos, es mediante el <strong>algoritmo de búsqueda en anchura (BFS)</strong>. Este algoritmo no solo permite encontrar un árbol generador, sino también verificar si un grafo es <strong>bipartito</strong> (divisible en dos conjuntos de vértices, A y B, donde no hay aristas entre vértices del mismo conjunto).</p>\n",
        "\n",
        "    <h3>Pasos del Algoritmo BFS para Encontrar un Árbol Generador</h3>\n",
        "    <ol>\n",
        "        <li><strong>Seleccionar un vértice inicial</strong> <code>v<sub>0</sub></code>: Elegimos cualquier vértice <code>v<sub>0</sub></code> del grafo <code>G</code> como la raíz del árbol generador.</li>\n",
        "        <li><strong>Construcción del árbol por niveles</strong>:\n",
        "            <ul>\n",
        "                <li>Colocamos <code>v<sub>0</sub></code> en el nivel 0 del árbol.</li>\n",
        "                <li>Identificamos todos los vértices vecinos de <code>v<sub>0</sub></code> (distancia 1), y los agregamos al siguiente nivel del árbol.</li>\n",
        "                <li>Repetimos el proceso con los vecinos de los vecinos, añadiendo vértices a niveles sucesivos según su distancia mínima a <code>v<sub>0</sub></code>.</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li><strong>Verificación de conectividad</strong>: Si el conjunto de vértices en el árbol es igual al conjunto total de vértices de <code>G</code>, entonces hemos completado el árbol generador.</li>\n",
        "        <li><strong>Añadir aristas</strong>: En cada paso, se elige un vértice <code>v<sub>i</sub></code> que ya está en el árbol y se agrega una arista hacia su vecino <code>w</code> que aún no está en el árbol.</li>\n",
        "    </ol>\n",
        "\n",
        "    <h2>Ejemplo del Diámetro y Radio de un Grafo</h2>\n",
        "    <p>El <strong>diámetro</strong> de un grafo es la máxima distancia entre dos vértices en un grafo conexo. Si el camino más largo entre dos vértices tiene una longitud de 4, entonces el diámetro es 4.</p>\n",
        "\n",
        "    <p>El <strong>radio</strong> de un grafo es la mínima distancia <code>r</code> tal que todos los vértices están como máximo a una distancia <code>r</code> de algún vértice central. En un grafo con radio 2, todos los vértices están a lo sumo a una distancia de 2 de un vértice particular.</p>\n",
        "\n",
        "    <h2>Complejidad del Algoritmo</h2>\n",
        "    <p>El tiempo de ejecución del algoritmo BFS es <code>O(V(G) + E(G))</code>, donde:</p>\n",
        "    <ul>\n",
        "        <li><code>V(G)</code>: Es el número de vértices en el grafo.</li>\n",
        "        <li><code>E(G)</code>: Es el número de aristas.</li>\n",
        "    </ul>\n",
        "    <p>Esto se debe a que cada vértice se visita una vez, y cada arista se explora una vez para asegurar que todos los vértices se hayan conectado.</p>\n",
        "\n",
        "    <h2>Resumen</h2>\n",
        "    <ul>\n",
        "        <li><strong>Proposición 3.1.3:</strong> Todo grafo conexo contiene un árbol generador.</li>\n",
        "        <li><strong>Búsqueda en Anchura (BFS):</strong> Un algoritmo eficiente para construir un árbol generador y verificar la bipartición de un grafo.</li>\n",
        "        <li>El algoritmo funciona explorando los vecinos de un vértice inicial en orden de cercanía (distancia), agregando vértices al árbol a medida que se avanza.</li>\n",
        "    </ul>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.core.display import display, HTML\n",
        "\n",
        "# Contenido HTML para la Explicación del Árbol BFS\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Árbol de Búsqueda en Anchura (BFS)</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: Arial, sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2E8B57;\n",
        "            margin-top: 20px;\n",
        "        }\n",
        "        h1 {\n",
        "            font-size: 2.5em;\n",
        "            text-align: center;\n",
        "        }\n",
        "        h2 {\n",
        "            font-size: 1.8em;\n",
        "        }\n",
        "        h3 {\n",
        "            font-size: 1.5em;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: disc;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        code {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 2px 4px;\n",
        "            font-family: Consolas, \"Courier New\", monospace;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1em;\n",
        "            overflow-x: auto;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "\n",
        "    <h1>Árbol de Búsqueda en Anchura (BFS)</h1>\n",
        "\n",
        "    <p>Las figuras 3.2 y 3.3 muestran cómo se construye un <strong>árbol de búsqueda en anchura (BFS)</strong> a partir de un grafo y cómo se organizan los niveles de los vértices en función de su distancia a un vértice raíz.</p>\n",
        "\n",
        "    <h2>Explicación del Ejemplo</h2>\n",
        "    <p>En el <strong>Ejemplo 10</strong>, el grafo tiene 9 vértices numerados del 1 al 9. Las aristas representan las conexiones entre ellos. El vértice <code>1</code> es seleccionado como la raíz para iniciar el proceso de búsqueda en anchura (BFS).</p>\n",
        "\n",
        "    <h2>Proceso de la Búsqueda en Anchura</h2>\n",
        "\n",
        "    <h3>Vértice raíz</h3>\n",
        "    <p>Se comienza en el vértice <code>1</code>, que es el primero en ser visitado y se considera el <strong>nivel 0</strong> del árbol de BFS.</p>\n",
        "\n",
        "    <h3>Nivel 1 (N1)</h3>\n",
        "    <p>Desde el vértice <code>1</code>, se exploran sus vecinos inmediatos, los vértices <code>3</code> y <code>9</code>. Estos vértices se colocan en el <strong>nivel 1</strong> del árbol, ya que están a una distancia de 1 arista desde el vértice raíz.</p>\n",
        "\n",
        "    <h3>Nivel 2 (N2)</h3>\n",
        "    <p>A continuación, se exploran los vecinos de los vértices del nivel 1. Los vecinos del vértice <code>3</code> son <code>2</code> y <code>6</code>, mientras que el vértice <code>9</code> tiene como vecino a <code>8</code>. Estos vértices se colocan en el <strong>nivel 2</strong> del árbol.</p>\n",
        "\n",
        "    <h3>Nivel 3 (N3)</h3>\n",
        "    <p>Finalmente, se exploran los vecinos de los vértices del nivel 2. Los vértices <code>2</code> y <code>6</code> tienen como vecinos a <code>4</code>, <code>7</code> y <code>5</code>, que se añaden al <strong>nivel 3</strong>.</p>\n",
        "\n",
        "    <h2>Representación del Árbol de BFS</h2>\n",
        "    <p>La Figura 3.2 muestra el grafo original con las aristas que se explorarán mediante el algoritmo de BFS. La Figura 3.3 muestra el resultado del árbol BFS después de recorrer el grafo. Las aristas que forman el árbol BFS están resaltadas y dirigidas, mostrando cómo se exploran los vértices en niveles a partir del vértice raíz <code>1</code>.</p>\n",
        "\n",
        "    <h2>Conjunto de vecinos <code>N<sub>i</sub>(v)</code></h2>\n",
        "    <p>Los conjuntos <code>N<sub>i</sub>(v)</code> representan los vértices que se encuentran a una distancia específica <code>i</code> desde el vértice raíz <code>v</code>.</p>\n",
        "    <ul>\n",
        "        <li><code>N<sub>1</sub>(1) = {3, 9}</code>: Estos vértices están a una distancia de 1 arista desde el vértice raíz <code>1</code>.</li>\n",
        "        <li><code>N<sub>2</sub>(1) = {2, 6, 8}</code>: Estos vértices están a una distancia de 2 aristas desde el vértice raíz <code>1</code>.</li>\n",
        "        <li><code>N<sub>3</sub>(1) = {4, 5, 7}</code>: Estos vértices están a una distancia de 3 aristas desde el vértice raíz.</li>\n",
        "    </ul>\n",
        "\n",
        "    <h2>Secuencia de Exploración</h2>\n",
        "    <p>La secuencia en la que se descubren los vértices durante la búsqueda en anchura es:</p>\n",
        "    <pre>(1, 3, 9, 2, 6, 8, 4, 7, 5)</pre>\n",
        "    <p>Esta secuencia refleja cómo el algoritmo visita los vértices siguiendo un orden basado en la distancia mínima desde el vértice raíz.</p>\n",
        "\n",
        "    <h2>Conclusión</h2>\n",
        "    <p>El <strong>algoritmo de búsqueda en anchura (BFS)</strong> recorre un grafo en niveles, comenzando desde un vértice raíz y explorando todos los vértices adyacentes en cada paso antes de pasar al siguiente nivel de vértices. El resultado es un <strong>árbol de BFS</strong> que conecta todos los vértices del grafo original y organiza los vértices en función de su distancia mínima al vértice raíz.</p>\n",
        "    <p>Este método no solo permite encontrar un <strong>árbol generador</strong>, sino que también es útil para determinar si un grafo es bipartito y para calcular otras propiedades, como el <strong>diámetro</strong> y el <strong>radio</strong> de un grafo.</p>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "KBsV8a5I-4pM",
        "outputId": "83564a69-5b96-41e5-e4eb-945de82fb648"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Árbol de Búsqueda en Anchura (BFS)</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: Arial, sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2E8B57;\n",
              "            margin-top: 20px;\n",
              "        }\n",
              "        h1 {\n",
              "            font-size: 2.5em;\n",
              "            text-align: center;\n",
              "        }\n",
              "        h2 {\n",
              "            font-size: 1.8em;\n",
              "        }\n",
              "        h3 {\n",
              "            font-size: 1.5em;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: disc;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        code {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 2px 4px;\n",
              "            font-family: Consolas, \"Courier New\", monospace;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1em;\n",
              "            overflow-x: auto;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "\n",
              "    <h1>Árbol de Búsqueda en Anchura (BFS)</h1>\n",
              "\n",
              "    <p>Las figuras 3.2 y 3.3 muestran cómo se construye un <strong>árbol de búsqueda en anchura (BFS)</strong> a partir de un grafo y cómo se organizan los niveles de los vértices en función de su distancia a un vértice raíz.</p>\n",
              "\n",
              "    <h2>Explicación del Ejemplo</h2>\n",
              "    <p>En el <strong>Ejemplo 10</strong>, el grafo tiene 9 vértices numerados del 1 al 9. Las aristas representan las conexiones entre ellos. El vértice <code>1</code> es seleccionado como la raíz para iniciar el proceso de búsqueda en anchura (BFS).</p>\n",
              "\n",
              "    <h2>Proceso de la Búsqueda en Anchura</h2>\n",
              "    \n",
              "    <h3>Vértice raíz</h3>\n",
              "    <p>Se comienza en el vértice <code>1</code>, que es el primero en ser visitado y se considera el <strong>nivel 0</strong> del árbol de BFS.</p>\n",
              "\n",
              "    <h3>Nivel 1 (N1)</h3>\n",
              "    <p>Desde el vértice <code>1</code>, se exploran sus vecinos inmediatos, los vértices <code>3</code> y <code>9</code>. Estos vértices se colocan en el <strong>nivel 1</strong> del árbol, ya que están a una distancia de 1 arista desde el vértice raíz.</p>\n",
              "\n",
              "    <h3>Nivel 2 (N2)</h3>\n",
              "    <p>A continuación, se exploran los vecinos de los vértices del nivel 1. Los vecinos del vértice <code>3</code> son <code>2</code> y <code>6</code>, mientras que el vértice <code>9</code> tiene como vecino a <code>8</code>. Estos vértices se colocan en el <strong>nivel 2</strong> del árbol.</p>\n",
              "\n",
              "    <h3>Nivel 3 (N3)</h3>\n",
              "    <p>Finalmente, se exploran los vecinos de los vértices del nivel 2. Los vértices <code>2</code> y <code>6</code> tienen como vecinos a <code>4</code>, <code>7</code> y <code>5</code>, que se añaden al <strong>nivel 3</strong>.</p>\n",
              "\n",
              "    <h2>Representación del Árbol de BFS</h2>\n",
              "    <p>La Figura 3.2 muestra el grafo original con las aristas que se explorarán mediante el algoritmo de BFS. La Figura 3.3 muestra el resultado del árbol BFS después de recorrer el grafo. Las aristas que forman el árbol BFS están resaltadas y dirigidas, mostrando cómo se exploran los vértices en niveles a partir del vértice raíz <code>1</code>.</p>\n",
              "\n",
              "    <h2>Conjunto de vecinos <code>N<sub>i</sub>(v)</code></h2>\n",
              "    <p>Los conjuntos <code>N<sub>i</sub>(v)</code> representan los vértices que se encuentran a una distancia específica <code>i</code> desde el vértice raíz <code>v</code>.</p>\n",
              "    <ul>\n",
              "        <li><code>N<sub>1</sub>(1) = {3, 9}</code>: Estos vértices están a una distancia de 1 arista desde el vértice raíz <code>1</code>.</li>\n",
              "        <li><code>N<sub>2</sub>(1) = {2, 6, 8}</code>: Estos vértices están a una distancia de 2 aristas desde el vértice raíz <code>1</code>.</li>\n",
              "        <li><code>N<sub>3</sub>(1) = {4, 5, 7}</code>: Estos vértices están a una distancia de 3 aristas desde el vértice raíz.</li>\n",
              "    </ul>\n",
              "\n",
              "    <h2>Secuencia de Exploración</h2>\n",
              "    <p>La secuencia en la que se descubren los vértices durante la búsqueda en anchura es:</p>\n",
              "    <pre>(1, 3, 9, 2, 6, 8, 4, 7, 5)</pre>\n",
              "    <p>Esta secuencia refleja cómo el algoritmo visita los vértices siguiendo un orden basado en la distancia mínima desde el vértice raíz.</p>\n",
              "\n",
              "    <h2>Conclusión</h2>\n",
              "    <p>El <strong>algoritmo de búsqueda en anchura (BFS)</strong> recorre un grafo en niveles, comenzando desde un vértice raíz y explorando todos los vértices adyacentes en cada paso antes de pasar al siguiente nivel de vértices. El resultado es un <strong>árbol de BFS</strong> que conecta todos los vértices del grafo original y organiza los vértices en función de su distancia mínima al vértice raíz.</p>\n",
              "    <p>Este método no solo permite encontrar un <strong>árbol generador</strong>, sino que también es útil para determinar si un grafo es bipartito y para calcular otras propiedades, como el <strong>diámetro</strong> y el <strong>radio</strong> de un grafo.</p>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Crear el grafo\n",
        "G = nx.Graph()\n",
        "edges = [(1, 3), (1, 9), (3, 2), (3, 6), (9, 6), (9, 8), (6, 4), (6, 7), (8, 5)]\n",
        "G.add_edges_from(edges)\n",
        "\n",
        "# Aplicar BFS desde el nodo 1\n",
        "bfs_tree = nx.bfs_tree(G, source=1)\n",
        "\n",
        "# Definir las posiciones de los nodos para visualización\n",
        "pos = {\n",
        "    1: (0, 3),\n",
        "    3: (-1, 2),\n",
        "    9: (1, 2),\n",
        "    2: (-2, 1),\n",
        "    6: (0, 1),\n",
        "    8: (2, 1),\n",
        "    4: (-1, 0),\n",
        "    7: (1, 0),\n",
        "    5: (2, 0)\n",
        "}\n",
        "\n",
        "# Dibujar el grafo y el árbol BFS\n",
        "plt.figure(figsize=(8, 6))\n",
        "\n",
        "# Dibujar el grafo completo en azul claro\n",
        "nx.draw(G, pos, with_labels=True, node_color='lightgray', edge_color='lightblue', node_size=800, font_size=14, font_weight='bold')\n",
        "\n",
        "# Resaltar el árbol BFS en negro\n",
        "nx.draw(bfs_tree, pos, with_labels=True, node_color='lightgray', edge_color='black', node_size=800, font_size=14, font_weight='bold')\n",
        "\n",
        "plt.title(\"Árbol de Búsqueda en Amplitud (BFS)\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 661
        },
        "id": "4ulH3g_v_82A",
        "outputId": "e54b1e57-584d-4120-a004-6bf62dd1981e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Crear el grafo\n",
        "G = nx.Graph()\n",
        "edges = [(1, 3), (1, 9), (3, 2), (3, 6), (9, 6), (9, 8), (6, 4), (6, 7), (8, 5)]\n",
        "G.add_edges_from(edges)\n",
        "\n",
        "# Aplicar BFS desde el nodo 1\n",
        "bfs_tree = nx.bfs_tree(G, source=1)\n",
        "\n",
        "# Obtener niveles de BFS (distancias desde el nodo raíz)\n",
        "levels = nx.single_source_shortest_path_length(G, source=1)\n",
        "\n",
        "# Definir colores para cada nivel\n",
        "level_colors = {\n",
        "    0: 'lightgreen',  # Nivel 0 (nodo raíz)\n",
        "    1: 'lightblue',   # Nivel 1\n",
        "    2: 'orange',      # Nivel 2\n",
        "    3: 'red'          # Nivel 3\n",
        "}\n",
        "\n",
        "# Crear una lista de colores para los nodos basados en el nivel\n",
        "node_colors = [level_colors[levels[node]] for node in G.nodes()]\n",
        "\n",
        "# Definir las posiciones de los nodos para visualización\n",
        "pos = {\n",
        "    1: (0, 3),\n",
        "    3: (-1, 2),\n",
        "    9: (1, 2),\n",
        "    2: (-2, 1),\n",
        "    6: (0, 1),\n",
        "    8: (2, 1),\n",
        "    4: (-1, 0),\n",
        "    7: (1, 0),\n",
        "    5: (2, 0)\n",
        "}\n",
        "\n",
        "# Dibujar el grafo y el árbol BFS\n",
        "plt.figure(figsize=(8, 6))\n",
        "\n",
        "# Dibujar el grafo completo en azul claro\n",
        "nx.draw(G, pos, with_labels=True, node_color=node_colors, edge_color='lightblue', node_size=800, font_size=14, font_weight='bold')\n",
        "\n",
        "# Resaltar el árbol BFS en negro\n",
        "nx.draw(bfs_tree, pos, with_labels=True, node_color=node_colors, edge_color='black', node_size=800, font_size=14, font_weight='bold')\n",
        "\n",
        "plt.title(\"Árbol de Búsqueda en Amplitud (BFS) con Niveles de Colores\")\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 661
        },
        "id": "0LAWMuUiAV65",
        "outputId": "703de127-6d39-4bd9-c4c7-efd42574882d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "from PIL import Image\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Subir el archivo\n",
        "uploaded = files.upload()\n",
        "\n",
        "# Abre la imagen\n",
        "for filename in uploaded.keys():\n",
        "    img = Image.open(filename)\n",
        "    plt.imshow(img)\n",
        "    plt.axis('off')  # Oculta los ejes\n",
        "    plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 422
        },
        "id": "JH_bnqCU4IEy",
        "outputId": "c6c25729-adde-4fe5-d215-f12da53e8ae3"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-ba774032-d180-4e1c-8069-02ad43c798c5\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-ba774032-d180-4e1c-8069-02ad43c798c5\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving GRAFO DE PETERSEN.png to GRAFO DE PETERSEN.png\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.core.display import display, HTML\n",
        "\n",
        "# Contenido HTML para la descripción del Grafo de Petersen y BFS\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Árbol Generador en el Grafo de Petersen</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: Arial, sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2E8B57;\n",
        "            margin-top: 20px;\n",
        "        }\n",
        "        h1 {\n",
        "            font-size: 2.5em;\n",
        "            text-align: center;\n",
        "        }\n",
        "        h2 {\n",
        "            font-size: 1.8em;\n",
        "        }\n",
        "        h3 {\n",
        "            font-size: 1.5em;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: disc;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        code {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 2px 4px;\n",
        "            font-family: Consolas, \"Courier New\", monospace;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #f4f4f4;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1em;\n",
        "            overflow-x: auto;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "\n",
        "    <h1>Árbol Generador en el Grafo de Petersen</h1>\n",
        "\n",
        "    <h2>Descripción del Grafo de Petersen (Figura 3.4)</h2>\n",
        "    <p>El <strong>grafo de Petersen</strong> consta de 10 vértices numerados del 1 al 10, y las aristas que conectan los vértices están organizadas en un patrón que forma un grafo <strong>no planar</strong> (no puede dibujarse en el plano sin que sus aristas se crucen). Este grafo es simétrico y tiene varias propiedades interesantes, como que <strong>no es bipartito</strong> y que tiene un alto grado de conectividad.</p>\n",
        "\n",
        "    <h2>Aplicación del Algoritmo de Búsqueda en Anchura (BFS)</h2>\n",
        "\n",
        "    <h3>Vértice raíz: 1</h3>\n",
        "    <p>Se selecciona el vértice <strong>1</strong> como el vértice raíz del árbol de búsqueda en anchura. A partir de este vértice, se exploran sus vecinos más cercanos en orden creciente de sus etiquetas.</p>\n",
        "\n",
        "    <h3>Exploración de los vecinos de <code>1</code></h3>\n",
        "    <p>Los vecinos del vértice <code>1</code> son los vértices <code>2</code>, <code>5</code> y <code>9</code>. Estos se agregan al primer nivel del árbol generador y las aristas correspondientes son:</p>\n",
        "    <pre>{1, 2}, {1, 5}, {1, 9}</pre>\n",
        "\n",
        "    <h3>Exploración de los vecinos de <code>2</code></h3>\n",
        "    <p>Luego, se pasa a explorar el primer vecino añadido al árbol, que es el vértice <code>2</code>. Sus vecinos más cercanos (que no están en el árbol aún) son <code>6</code> y <code>7</code>. Las aristas añadidas al árbol son:</p>\n",
        "    <pre>{2, 6}, {2, 7}</pre>\n",
        "\n",
        "    <h3>Exploración de los vecinos de <code>5</code></h3>\n",
        "    <p>A continuación, se exploran los vecinos del vértice <code>5</code>. Sus vecinos que aún no están en el árbol son <code>3</code> y <code>8</code>, y las aristas añadidas son:</p>\n",
        "    <pre>{5, 3}, {5, 8}</pre>\n",
        "\n",
        "    <h3>Exploración de los vecinos de <code>9</code></h3>\n",
        "    <p>Finalmente, se exploran los vecinos del vértice <code>9</code>. Los vértices <code>4</code> y <code>10</code> aún no están en el árbol, por lo que se añaden con las siguientes aristas:</p>\n",
        "    <pre>{9, 4}, {9, 10}</pre>\n",
        "\n",
        "    <h2>Árbol Generador Final</h2>\n",
        "    <p>El proceso finaliza cuando todos los vértices han sido añadidos al árbol generador. Las aristas totales del árbol son:</p>\n",
        "    <pre>{1, 2}, {1, 5}, {1, 9}, {2, 6}, {2, 7}, {5, 3}, {5, 8}, {9, 4}, {9, 10}</pre>\n",
        "\n",
        "    <h2>Organización del Árbol en Niveles (Capas del Árbol)</h2>\n",
        "    <p>El árbol de BFS obtenido está organizado en niveles, donde <code>N<sub>i</sub>(v)</code> representa el conjunto de vértices que están a una distancia <code>i</code> del vértice raíz <code>v</code> (en este caso, el vértice 1):</p>\n",
        "    <ul>\n",
        "        <li><code>N<sub>0</sub>(1) = {1}</code>: El vértice raíz.</li>\n",
        "        <li><code>N<sub>1</sub>(1) = {2, 5, 9}</code>: Los vértices que están a una distancia de 1 arista del vértice raíz.</li>\n",
        "        <li><code>N<sub>2</sub>(1) = {6, 7, 3, 8, 4, 10}</code>: Los vértices que están a una distancia de 2 aristas del vértice raíz.</li>\n",
        "    </ul>\n",
        "\n",
        "    <h2>Propiedades del Grafo de Petersen</h2>\n",
        "    <ul>\n",
        "        <li><strong>Diámetro:</strong> El diámetro del grafo de Petersen es 2. La mayor distancia posible entre dos vértices cualesquiera es 2.</li>\n",
        "        <li><strong>Radio:</strong> El radio también es 2, lo que significa que todos los vértices están a una distancia máxima de 2 aristas desde el vértice central.</li>\n",
        "    </ul>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "V9WFIKTLDBNZ",
        "outputId": "f03566ec-91fc-4e4c-c856-4512317c2d14"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Árbol Generador en el Grafo de Petersen</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: Arial, sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2E8B57;\n",
              "            margin-top: 20px;\n",
              "        }\n",
              "        h1 {\n",
              "            font-size: 2.5em;\n",
              "            text-align: center;\n",
              "        }\n",
              "        h2 {\n",
              "            font-size: 1.8em;\n",
              "        }\n",
              "        h3 {\n",
              "            font-size: 1.5em;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: disc;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        code {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 2px 4px;\n",
              "            font-family: Consolas, \"Courier New\", monospace;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #f4f4f4;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1em;\n",
              "            overflow-x: auto;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "\n",
              "    <h1>Árbol Generador en el Grafo de Petersen</h1>\n",
              "\n",
              "    <h2>Descripción del Grafo de Petersen (Figura 3.4)</h2>\n",
              "    <p>El <strong>grafo de Petersen</strong> consta de 10 vértices numerados del 1 al 10, y las aristas que conectan los vértices están organizadas en un patrón que forma un grafo <strong>no planar</strong> (no puede dibujarse en el plano sin que sus aristas se crucen). Este grafo es simétrico y tiene varias propiedades interesantes, como que <strong>no es bipartito</strong> y que tiene un alto grado de conectividad.</p>\n",
              "\n",
              "    <h2>Aplicación del Algoritmo de Búsqueda en Anchura (BFS)</h2>\n",
              "\n",
              "    <h3>Vértice raíz: 1</h3>\n",
              "    <p>Se selecciona el vértice <strong>1</strong> como el vértice raíz del árbol de búsqueda en anchura. A partir de este vértice, se exploran sus vecinos más cercanos en orden creciente de sus etiquetas.</p>\n",
              "\n",
              "    <h3>Exploración de los vecinos de <code>1</code></h3>\n",
              "    <p>Los vecinos del vértice <code>1</code> son los vértices <code>2</code>, <code>5</code> y <code>9</code>. Estos se agregan al primer nivel del árbol generador y las aristas correspondientes son:</p>\n",
              "    <pre>{1, 2}, {1, 5}, {1, 9}</pre>\n",
              "\n",
              "    <h3>Exploración de los vecinos de <code>2</code></h3>\n",
              "    <p>Luego, se pasa a explorar el primer vecino añadido al árbol, que es el vértice <code>2</code>. Sus vecinos más cercanos (que no están en el árbol aún) son <code>6</code> y <code>7</code>. Las aristas añadidas al árbol son:</p>\n",
              "    <pre>{2, 6}, {2, 7}</pre>\n",
              "\n",
              "    <h3>Exploración de los vecinos de <code>5</code></h3>\n",
              "    <p>A continuación, se exploran los vecinos del vértice <code>5</code>. Sus vecinos que aún no están en el árbol son <code>3</code> y <code>8</code>, y las aristas añadidas son:</p>\n",
              "    <pre>{5, 3}, {5, 8}</pre>\n",
              "\n",
              "    <h3>Exploración de los vecinos de <code>9</code></h3>\n",
              "    <p>Finalmente, se exploran los vecinos del vértice <code>9</code>. Los vértices <code>4</code> y <code>10</code> aún no están en el árbol, por lo que se añaden con las siguientes aristas:</p>\n",
              "    <pre>{9, 4}, {9, 10}</pre>\n",
              "\n",
              "    <h2>Árbol Generador Final</h2>\n",
              "    <p>El proceso finaliza cuando todos los vértices han sido añadidos al árbol generador. Las aristas totales del árbol son:</p>\n",
              "    <pre>{1, 2}, {1, 5}, {1, 9}, {2, 6}, {2, 7}, {5, 3}, {5, 8}, {9, 4}, {9, 10}</pre>\n",
              "\n",
              "    <h2>Organización del Árbol en Niveles (Capas del Árbol)</h2>\n",
              "    <p>El árbol de BFS obtenido está organizado en niveles, donde <code>N<sub>i</sub>(v)</code> representa el conjunto de vértices que están a una distancia <code>i</code> del vértice raíz <code>v</code> (en este caso, el vértice 1):</p>\n",
              "    <ul>\n",
              "        <li><code>N<sub>0</sub>(1) = {1}</code>: El vértice raíz.</li>\n",
              "        <li><code>N<sub>1</sub>(1) = {2, 5, 9}</code>: Los vértices que están a una distancia de 1 arista del vértice raíz.</li>\n",
              "        <li><code>N<sub>2</sub>(1) = {6, 7, 3, 8, 4, 10}</code>: Los vértices que están a una distancia de 2 aristas del vértice raíz.</li>\n",
              "    </ul>\n",
              "\n",
              "    <h2>Propiedades del Grafo de Petersen</h2>\n",
              "    <ul>\n",
              "        <li><strong>Diámetro:</strong> El diámetro del grafo de Petersen es 2. La mayor distancia posible entre dos vértices cualesquiera es 2.</li>\n",
              "        <li><strong>Radio:</strong> El radio también es 2, lo que significa que todos los vértices están a una distancia máxima de 2 aristas desde el vértice central.</li>\n",
              "    </ul>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import networkx as nx\n",
        "import numpy as np\n",
        "\n",
        "# Crear el Grafo de Petersen\n",
        "G = nx.petersen_graph()\n",
        "\n",
        "# Definir la disposición exacta de los nodos basada en la imagen proporcionada\n",
        "pos = {\n",
        "    0: (0, 1.5),    # Nodo 1\n",
        "    1: (-1.4, 0.5), # Nodo 2\n",
        "    2: (-0.8, -1.2),# Nodo 3\n",
        "    3: (0.8, -1.2), # Nodo 4\n",
        "    4: (1.4, 0.5),  # Nodo 5\n",
        "    5: (0, 0.6),    # Nodo 6\n",
        "    6: (-0.5, 0.2), # Nodo 7\n",
        "    7: (-0.4, -0.7),# Nodo 8\n",
        "    8: (0.4, -0.7), # Nodo 9\n",
        "    9: (0.5, 0.2)   # Nodo 10\n",
        "}\n",
        "\n",
        "# Crear un mapa de colores para las aristas\n",
        "edge_colors = np.linspace(0, 1, len(G.edges))\n",
        "edges = list(G.edges)\n",
        "\n",
        "# Dibujar el grafo con splines (curvas) para las aristas\n",
        "plt.figure(figsize=(8, 8))\n",
        "\n",
        "# Dibujar los nodos\n",
        "nx.draw_networkx_nodes(G, pos, node_color='black', node_size=700)\n",
        "\n",
        "# Dibujar etiquetas\n",
        "nx.draw_networkx_labels(G, pos, font_color='white', font_size=12)\n",
        "\n",
        "# Dibujar las aristas curvas con diferentes colores\n",
        "nx.draw_networkx_edges(\n",
        "    G, pos,\n",
        "    edgelist=edges,\n",
        "    edge_color=edge_colors,\n",
        "    edge_cmap=plt.cm.viridis,  # Usamos un mapa de colores (degradado)\n",
        "    width=2.5,\n",
        "    connectionstyle='arc3, rad=0.2'  # Las aristas se dibujan con curvas\n",
        ")\n",
        "\n",
        "# Mostrar el grafo\n",
        "plt.title('Grafo de Petersen con aristas dinámicas')\n",
        "plt.axis('off')  # Ocultar los ejes\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 858
        },
        "id": "LOTkU3yF462a",
        "outputId": "b9adcaae-8e12-4339-c08c-c2deefb8c32d"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-4-59dbc96a4195>:36: UserWarning: \n",
            "\n",
            "The connectionstyle keyword argument is not applicable when drawing edges\n",
            "with LineCollection.\n",
            "\n",
            "To make this warning go away, either specify `arrows=True` to\n",
            "force FancyArrowPatches or use the default values.\n",
            "Note that using FancyArrowPatches may be slow for large graphs.\n",
            "\n",
            "  nx.draw_networkx_edges(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ],
            "image/png": 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\n"
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    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "HdJXJOBQ837n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1. ¿Qué establece la Proposición 3.1.3 sobre los grafos conexos y los árboles generadores?\n",
        "La **Proposición 3.1.3** establece que todo grafo conexo contiene al menos un **árbol generador** (spanning tree). Esto significa que es posible encontrar un subgrafo acíclico que conecte todos los vértices del grafo original, conservando su conectividad.\n",
        "\n",
        "## 2. ¿Cómo se define un árbol generador en un grafo?\n",
        "Un **árbol generador** es un subgrafo de un grafo conexo que incluye todos los vértices del grafo original y es **acíclico** (sin ciclos). Además, tiene exactamente \\( V - 1 \\) aristas, donde \\( V \\) es el número de vértices del grafo.\n",
        "\n",
        "## 3. ¿Cuál es el proceso para encontrar un árbol generador en un grafo conexo?\n",
        "El proceso para encontrar un árbol generador implica identificar y eliminar ciclos del grafo. A medida que se detectan ciclos, se eliminan aristas hasta que el grafo queda sin ciclos y mantiene su conectividad, transformándose en un **árbol generador**.\n",
        "\n",
        "## 4. ¿Qué rol juegan los ciclos en la construcción de un árbol generador?\n",
        "Los **ciclos** se eliminan durante la construcción de un árbol generador. En un árbol generador no puede haber ciclos, ya que estos introducirían redundancia en la conectividad. El proceso implica encontrar ciclos y eliminar una arista de cada ciclo hasta que el grafo se vuelva acíclico.\n",
        "\n",
        "## 5. ¿Qué es el algoritmo de Búsqueda en Anchura (BFS) y cómo se relaciona con los árboles generadores?\n",
        "El **algoritmo de Búsqueda en Anchura (BFS)** es un algoritmo que recorre un grafo **nivel por nivel**, comenzando desde un vértice inicial y explorando todos sus vecinos antes de pasar al siguiente nivel de vértices. Este algoritmo se puede usar para construir un **árbol generador**, conectando todos los vértices sin crear ciclos.\n",
        "\n",
        "## 6. ¿Cuáles son los pasos del algoritmo BFS para encontrar un árbol generador?\n",
        "Los pasos del algoritmo BFS para encontrar un árbol generador son:\n",
        "1. Seleccionar un vértice inicial \\( v_0 \\).\n",
        "2. Construir el árbol **nivel por nivel**, agregando los vecinos de cada vértice al nivel correspondiente.\n",
        "3. Verificar la **conectividad** del grafo.\n",
        "4. Añadir las aristas necesarias sin formar ciclos, completando así el árbol generador.\n",
        "\n",
        "## 7. ¿Cómo se selecciona el vértice inicial en el algoritmo BFS y por qué es importante?\n",
        "En el algoritmo BFS, se selecciona un vértice inicial \\( v_0 \\) de manera arbitraria, y este se utiliza como la **raíz del árbol**. La selección del vértice inicial es importante porque determina el punto de partida para la exploración de niveles en el árbol BFS.\n",
        "\n",
        "## 8. ¿Qué significa construir un árbol BFS por niveles?\n",
        "Construir un árbol BFS por niveles implica organizar los vértices en función de su **distancia** al vértice raíz \\( v_0 \\). Los vértices directamente conectados con \\( v_0 \\) forman el **nivel 1**, los vértices conectados con los vértices del nivel 1 forman el **nivel 2**, y así sucesivamente.\n",
        "\n",
        "## 9. ¿Cómo se verifica la conectividad de un grafo utilizando el algoritmo BFS?\n",
        "La conectividad se verifica en el algoritmo BFS al comprobar que **todos los vértices** del grafo original han sido visitados y añadidos al árbol BFS. Si todos los vértices están presentes en el árbol generador, el grafo es conexo.\n",
        "\n",
        "## 10. ¿Qué función cumplen las aristas en la construcción del árbol generador con BFS?\n",
        "Las aristas en el algoritmo BFS conectan los vértices en cada nivel del árbol, pero se seleccionan cuidadosamente para **evitar la creación de ciclos**. Solo se añaden aristas entre vértices que aún no están conectados en el árbol generador.\n",
        "\n",
        "## 11. ¿Cómo se define el diámetro de un grafo?\n",
        "El **diámetro de un grafo** es la distancia más larga entre dos vértices del grafo. Es decir, es la longitud del **camino más largo** entre cualquier par de vértices en el grafo conexo.\n",
        "\n",
        "## 12. ¿Qué es el radio de un grafo y cómo se calcula?\n",
        "El **radio de un grafo** es la mínima distancia \\( r \\) tal que todos los vértices del grafo están como máximo a esa distancia de un **vértice central**. Se calcula encontrando el vértice con la menor distancia máxima a todos los demás vértices.\n",
        "\n",
        "## 13. ¿Cuál es la complejidad temporal del algoritmo BFS y cómo se calcula?\n",
        "La **complejidad temporal** del algoritmo BFS es \\( O(V(G) + E(G)) \\), donde \\( V(G) \\) es el número de vértices y \\( E(G) \\) es el número de aristas en el grafo. Esta complejidad se debe a que el algoritmo visita cada vértice y explora cada arista una vez.\n",
        "\n",
        "## 14. ¿Qué propiedades del grafo se pueden determinar utilizando BFS, además del árbol generador?\n",
        "Además de construir un árbol generador, el algoritmo BFS puede determinar si un grafo es **bipartito** (si se puede dividir en dos conjuntos sin aristas internas) y puede calcular otras propiedades como el **diámetro** y el **radio** del grafo.\n",
        "\n",
        "## 15. ¿Cómo se utiliza el algoritmo BFS para organizar un grafo en niveles?\n",
        "El algoritmo BFS organiza un grafo en niveles comenzando desde un **vértice raíz**. Los vecinos inmediatos del vértice raíz forman el **primer nivel**, los vecinos de estos forman el **segundo nivel**, y así sucesivamente, creando una jerarquía basada en distancias.\n",
        "\n",
        "## 16. ¿Qué es el grafo de Petersen y cuáles son sus características?\n",
        "El **grafo de Petersen** es un grafo no planar con 10 vértices y 15 aristas. Tiene varias propiedades interesantes, como que **no es bipartito**, tiene un **diámetro de 2**, y una alta **conectividad**, lo que lo convierte en un grafo ampliamente estudiado en teoría de grafos.\n",
        "\n",
        "## 17. ¿Cómo se aplica el algoritmo BFS al grafo de Petersen para encontrar un árbol generador?\n",
        "En el grafo de Petersen, el algoritmo BFS se aplica seleccionando un vértice raíz (por ejemplo, el vértice 1), y luego explorando sus vecinos nivel por nivel, añadiendo aristas entre los vértices que no crean ciclos, hasta completar el árbol generador.\n",
        "\n",
        "## 18. ¿Cómo se organizan los vértices del grafo de Petersen en niveles mediante BFS?\n",
        "Los vértices del grafo de Petersen se organizan en niveles basados en su **distancia al vértice raíz**. Los vecinos del vértice raíz forman el **nivel 1**, los vecinos de los vértices del nivel 1 forman el **nivel 2**, y así sucesivamente hasta incluir todos los vértices.\n",
        "\n",
        "## 19. ¿Qué significa que el grafo de Petersen tiene un diámetro de 2 y un radio de 2?\n",
        "El **diámetro de 2** significa que la distancia más larga entre dos vértices del grafo es de 2 aristas. El **radio de 2** indica que todos los vértices están a una distancia máxima de 2 aristas desde un **vértice central**.\n",
        "\n",
        "## 20. ¿Cómo se visualizan los niveles y aristas en un árbol BFS construido a partir de un grafo?\n",
        "Los niveles y aristas en un árbol BFS se visualizan colocando el **vértice raíz** en el nivel 0 y organizando los demás vértices en niveles según su **distancia al vértice raíz**. Las aristas conectan los vértices entre niveles, resaltando las conexiones sin crear ciclos.\n"
      ],
      "metadata": {
        "id": "SaRrQ_DJ7yhv"
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