{"id":10600,"date":"2020-11-01T19:46:11","date_gmt":"2020-11-01T18:46:11","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=10600"},"modified":"2022-12-03T23:05:29","modified_gmt":"2022-12-03T22:05:29","slug":"corrected-exercises-graph-theory-basics","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/","title":{"rendered":"Ejercicios corregidos: conceptos b\u00e1sicos de la teor\u00eda de grafos"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"10600\" class=\"elementor elementor-10600\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a2d10d6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a2d10d6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-fc4bb75\" data-id=\"fc4bb75\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fadbed9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"fadbed9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Teor\u00eda de grafos<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-af05c55\" data-id=\"af05c55\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ff558a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1ff558a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c6d6863\" data-id=\"c6d6863\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5615aca elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5615aca\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/en.wikipedia.org\/wiki\/Graph_theory\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-60b7f76 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"60b7f76\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d8b4809\" data-id=\"d8b4809\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-04a9416 elementor-widget elementor-widget-heading\" data-id=\"04a9416\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Corrected-exercises-on-graph-theory-basics\" >Ejercicios corregidos sobre los conceptos b\u00e1sicos de la teor\u00eda de grafos.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Modeling-with-graph-theory\" >Modelado con teor\u00eda de grafos<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-1\" >Ejercicio 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-2\" >Ejercicio 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-4\" >Ejercicio 4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-5\" >Ejercicio 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-6\" >Ejercicio 6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Modeling-with-tree\" >Modelado con \u00e1rbol<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-7\" >Ejercicio 7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/complex-systems-ai.com\/es\/teoria-de-grafos\/ejercicios-corregidos-teoria-de-grafos-basicos\/#Exercise-8\" >Ejercicio 8<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Corrected-exercises-on-graph-theory-basics\"><\/span>Ejercicios corregidos sobre los conceptos b\u00e1sicos de la teor\u00eda de grafos.<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c1484c1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c1484c1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1c6140b\" data-id=\"1c6140b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6912221 elementor-widget elementor-widget-text-editor\" data-id=\"6912221\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Esta p\u00e1gina muestra algunos ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos. El objetivo de estos ejercicios es aprender a modelar un problema a trav\u00e9s de conceptos b\u00e1sicos y de teor\u00eda de grafos.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6c8abb0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c8abb0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4a72134\" data-id=\"4a72134\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6b37cf5 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"6b37cf5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cbbe2dc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cbbe2dc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c98e0ec\" data-id=\"c98e0ec\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a1c8b92 elementor-widget elementor-widget-heading\" data-id=\"a1c8b92\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Modeling-with-graph-theory\"><\/span>Modelado con teor\u00eda de grafos<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ae97c3b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ae97c3b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5b7f0c6\" data-id=\"5b7f0c6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8aad4cb elementor-widget elementor-widget-text-editor\" data-id=\"8aad4cb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-1\"><\/span><strong><b>Ejercicio 1<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Dos jugadores tienen 2 o m\u00e1s lotes de partidos. En cada turno, el siguiente jugador puede eliminar varias coincidencias (seg\u00fan la regla seleccionada). El jugador que elimina el \u00faltimo partido pierde.<br \/>Modele este juego con un gr\u00e1fico en el caso en el que uno tenga dos montones que contengan cada uno tres partidos, y donde un jugador pueda eliminar uno o dos partidos cada uno.<br \/>\u00bfQu\u00e9 movimiento debe jugar el primer jugador para ganar el juego?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6a41ad5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6a41ad5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7940f05\" data-id=\"7940f05\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5f891a3 elementor-widget elementor-widget-toggle\" data-id=\"5f891a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1001\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1001\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1001\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1001\"><p><img decoding=\"async\" class=\"aligncenter wp-image-10608 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image129.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"319\" height=\"81\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image129.png 319w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image129-300x76.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p><p>Los bordes est\u00e1n orientados de izquierda a derecha. Si estamos en posici\u00f3n o ganamos. As\u00ed, la posici\u00f3n comprobar\u00e1 que, sea cual sea la jugada de tu adversario, puedes alcanzar o<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2b3b9b0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2b3b9b0\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d6ee68c\" data-id=\"d6ee68c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-29f63f2 elementor-widget elementor-widget-text-editor\" data-id=\"29f63f2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-2\"><\/span><strong><b>Ejercicio 2<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>El siguiente gr\u00e1fico muestra los pasillos de un museo. Un guardia colocado en un pasillo puede monitorear dos uniones colocadas en sus extremos. \u00bfCu\u00e1ntos guardias se necesitan (y c\u00f3mo colocarlos) para que se controlen todas las intersecciones?<br \/>Si ahora colocamos guardias en las intersecciones, asumiendo que un guardia puede monitorear todos los corredores que conducen a este cruce, \u00bfcu\u00e1ntos guardias se necesitan?<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-10609 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image130.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"193\" height=\"167\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dd0f515 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dd0f515\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e0928f1\" data-id=\"e0928f1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ccdb903 elementor-widget elementor-widget-toggle\" data-id=\"ccdb903\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2141\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2141\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2141\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2141\"><p>Cada guardia se colocar\u00e1 en un borde y podr\u00e1 monitorear dos intersecciones (v\u00e9rtices). El gr\u00e1fico tiene 11 v\u00e9rtices; se necesitar\u00e1n al menos seis guardias. Por lo tanto, debemos encontrar un conjunto (m\u00ednimo) de al menos seis aristas, de manera que cada v\u00e9rtice incida al menos a una de estas aristas. El siguiente gr\u00e1fico proporciona una soluci\u00f3n (bordes m\u00e1s gruesos).<\/p><p>Esta vez, los guardias est\u00e1n en los v\u00e9rtices y vigilan los bordes. Debe haber un conjunto de v\u00e9rtices tal que cada borde incida al menos en uno de estos v\u00e9rtices. El siguiente gr\u00e1fico proporciona una soluci\u00f3n utilizando 6 v\u00e9rtices (v\u00e9rtices blancos).<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-10610 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image131.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"194\" height=\"168\" title=\"\"><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-011ead6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"011ead6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55ac365\" data-id=\"55ac365\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-089f274 elementor-widget elementor-widget-text-editor\" data-id=\"089f274\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-4\"><\/span><strong><b>Ejercicio 4<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Skynet es una red con 15 v\u00e9rtices. Puede ir desde cada v\u00e9rtice hasta al menos otros siete v\u00e9rtices por enlace. \u00bfPodemos ir por enlace desde un v\u00e9rtice X a cada uno de los dem\u00e1s?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-94e1ffb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"94e1ffb\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b73f2d1\" data-id=\"b73f2d1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-45cc752 elementor-widget elementor-widget-toggle\" data-id=\"45cc752\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7311\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-7311\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-7311\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-7311\"><p>Sea A cualquier v\u00e9rtice. X est\u00e1 vinculado a al menos 7 ciudades diferentes. Entonces tenemos una red de 8 v\u00e9rtices conectados por enlaces. En un v\u00e9rtice, tambi\u00e9n puede conectarse a al menos otros siete v\u00e9rtices; Por tanto, existe una nueva red de 8 v\u00e9rtices. Debe haber un v\u00e9rtice compartido en estas redes, porque de lo contrario la red tendr\u00eda al menos 16 v\u00e9rtices. X est\u00e1 conectado a A como m\u00e1ximo en dos planos, a trav\u00e9s de este v\u00e9rtice com\u00fan; est\u00e1 conectado con todas las dem\u00e1s ciudades.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-366fd3d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"366fd3d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-adb48ac\" data-id=\"adb48ac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6738805 elementor-widget elementor-widget-text-editor\" data-id=\"6738805\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-5\"><\/span><strong><b>Ejercicio 5<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Una red est\u00e1 compuesta por siete plantas. Una ciudad est\u00e1 vinculada exactamente a dos plantas. Dos plantas comparten exactamente una ciudad. \u00bfA cu\u00e1ntas ciudades da servicio la red? Demuestre que una gr\u00e1fica completa con v\u00e9rtices tiene n (n-1) \/ 2 enlaces.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-27d5fc9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"27d5fc9\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ea88731\" data-id=\"ea88731\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-89ff41b elementor-widget elementor-widget-toggle\" data-id=\"89ff41b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1441\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1441\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1441\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1441\"><p>Las plantas son los v\u00e9rtices y las ciudades est\u00e1n representadas por un borde que conecta dos v\u00e9rtices. La regla 2 implica que no hay aristas m\u00faltiples y que cualquier par de v\u00e9rtices son adyacentes; es decir, que el gr\u00e1fico est\u00e9 completo; es k<sub>7<\/sub>, es decir, 21 enlaces.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-022cc4c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"022cc4c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-29a98f6\" data-id=\"29a98f6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6da734b elementor-widget elementor-widget-text-editor\" data-id=\"6da734b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-6\"><\/span><strong><b>Ejercicio 6<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Considerando el siguiente sistema matem\u00e1tico:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10611 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image132.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"243\" height=\"112\" title=\"\"><\/p><p>Donde es 0 o 1. Determine, con un problema gr\u00e1fico, una soluci\u00f3n que maximice la funci\u00f3n objetivo :.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ba9f3a7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ba9f3a7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-71cf199\" data-id=\"71cf199\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-78a0c03 elementor-widget elementor-widget-toggle\" data-id=\"78a0c03\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1261\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1261\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1261\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1261\"><p>El v\u00e9rtice representa una variable. Dos v\u00e9rtices est\u00e1n conectados si est\u00e1n en la misma desigualdad. El problema es encontrar un conjunto m\u00e1ximo de v\u00e9rtices donde ning\u00fan par de v\u00e9rtices tenga un v\u00ednculo directo.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10612 size-medium\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image133-300x139.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"300\" height=\"139\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image133-300x139.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image133.png 407w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-36ab21a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"36ab21a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-10ea4b1\" data-id=\"10ea4b1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e640868 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"e640868\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-82b4c45 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"82b4c45\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-57f4cc6\" data-id=\"57f4cc6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0946a0c elementor-widget elementor-widget-heading\" data-id=\"0946a0c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Modeling-with-tree\"><\/span>Modelado con \u00e1rbol<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-870b83c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"870b83c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2747adf\" data-id=\"2747adf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8a4969d elementor-widget elementor-widget-text-editor\" data-id=\"8a4969d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-7\"><\/span><strong><b>Ejercicio 7<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Sea un grafo no orientado con v\u00e9rtices. Demuestre que todas las siguientes propiedades son equivalentes:<\/p><ul><li>es un arbol<\/li><li>est\u00e1 conectado y si quitamos un borde, ya no est\u00e1 conectado<\/li><li>est\u00e1 conectado con el borde<\/li><li>no tiene ciclo hasta que agregamos una ventaja<\/li><li>no tiene ciclo con borde<\/li><li>Solo un camino entre cualquier par de v\u00e9rtices<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-79cb19c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"79cb19c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd0ecef\" data-id=\"dd0ecef\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d9b137 elementor-widget elementor-widget-text-editor\" data-id=\"7d9b137\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2><span class=\"ez-toc-section\" id=\"Exercise-8\"><\/span><strong><b>Ejercicio 8<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><p>Queremos agregar una bater\u00eda en una red. El siguiente gr\u00e1fico muestra el costo de enviar energ\u00eda entre dos subestaciones de la red y la cantidad de energ\u00eda enviada por una subestaci\u00f3n. Debe colocar la bater\u00eda en una subestaci\u00f3n minimizando el costo total.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10613 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image134.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"321\" height=\"157\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image134.png 321w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image134-300x147.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8d8dca8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d8dca8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4f1aa33\" data-id=\"4f1aa33\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1980b71 elementor-widget elementor-widget-toggle\" data-id=\"1980b71\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2671\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2671\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Soluci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2671\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2671\"><p>Calcule la suma de todos los costos en cada subestaci\u00f3n, es decir, el costo de cada camino entre cualquier subestaci\u00f3n a la subestaci\u00f3n elegida (borde * v\u00e9rtice).<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10614 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image135.png\" alt=\"Ejercicios corregidos sobre \u00e1rboles y modelado de teor\u00eda de grafos.\" width=\"402\" height=\"164\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image135.png 402w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/11\/Image135-300x122.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Graph Theory Home Wiki Ejercicios corregidos sobre los conceptos b\u00e1sicos de la teor\u00eda de grafos Esta p\u00e1gina muestra algunos ejercicios corregidos sobre el modelado y los \u00e1rboles de la teor\u00eda de grafos. T\u00e9 \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":2204,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10600","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/10600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=10600"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/10600\/revisions"}],"predecessor-version":[{"id":19064,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/10600\/revisions\/19064"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/2204"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=10600"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}