{"id":155256,"date":"2022-03-26T00:26:39","date_gmt":"2022-03-25T18:56:39","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/graph-theory-introduction-explanation-terminologies-and-faqs\/"},"modified":"2024-05-06T14:22:26","modified_gmt":"2024-05-06T08:52:26","slug":"graph-theory-introduction-explanation-terminologies-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/","title":{"rendered":"Graph Theory"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">Table of Contents<\/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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/#Introduction_to_Graph_Theory\" title=\"Introduction to Graph Theory\">Introduction to Graph Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/#History_of_Graph_Theory\" title=\"History of Graph Theory\">History of Graph Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/#Terminologies_of_Graph_Theory\" title=\"Terminologies of Graph Theory\">Terminologies of Graph Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/#Difference_Between_Circuit_and_Cycle_in_Graph_Theory\" title=\"Difference Between Circuit and Cycle in Graph Theory\">Difference Between Circuit and Cycle in Graph Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/graph-theory\/#Graph_Theory_and_Application_Question_Bank\" title=\"Graph Theory and Application Question Bank\">Graph Theory and Application Question Bank<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Graph_Theory\"><\/span>Introduction to Graph Theory<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Graph theory is the study of graphs and their properties. A graph consists of a set of vertices (or nodes) and a set of edges connecting them. The edges can be directed or undirected.<\/p>\n<p>Some basic properties of graphs include:<\/p>\n<p>\u2022 The degree of a vertex is the number of edges connected to it.<\/p>\n<p>\u2022 The shortest path between two vertices is called a shortest path or a path length or a distance.<\/p>\n<p>\u2022 The distance between two vertices is the length of the shortest path between them.<\/p>\n<p>\u2022 The connectivity of a graph is the number of pairs of vertices that can be connected by a path.<\/p>\n<p>\u2022 The degree sequence of a graph is a vector consisting of the degree of each vertex in order from the smallest to the largest.<\/p>\n<p>\u2022 The degree of a graph is the sum of the degrees of its vertices.<\/p>\n<p>\u2022 The degree of a graph is even if and only if its degree sequence is even.<\/p>\n<p>\u2022 The degree of a graph is odd if and only if its degree sequence is odd.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"History_of_Graph_Theory\"><\/span>History of Graph Theory<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Graph theory is the study of graphs and their properties. Graphs are mathematical structures consisting of vertices (or nodes) and edges connecting them. Graph theory is one of the oldest branches of mathematics, dating back to the 17th century.<\/p>\n<p>The first recorded use of the word \u201cgraph\u201d was by Sir William Hamilton in 1852. Hamilton introduced graph theory to study the properties of graphs associated with electrical circuits.<\/p>\n<p>In the early 20th century, graph theory began to be studied more intensively, and many of the basic concepts and results were established.<\/p>\n<p>One of the most important early results in graph theory was the four color theorem, which states that any graph can be colored using four colors so that no two adjacent vertices are the same color.<\/p>\n<p>Since the early days of graph theory, the subject has expanded to include a wide variety of topics, including network theory, transportation theory, and matchings.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Terminologies_of_Graph_Theory\"><\/span>Terminologies of Graph Theory<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In graph theory, a vertex (plural: vertices) is a point where two or more edges meet. An edge (plural: edges) is a line between two vertices.<\/p>\n<p>A graph is a collection of vertices and edges. The edges in a graph can be directed or undirected. A directed edge has a direction, from one vertex to another. An undirected edge has no direction.<\/p>\n<p>A graph is connected if there is a path between any two vertices in the graph. A graph is disconnected if there is no path between any two vertices in the graph.<\/p>\n<p>A graph is simple if it has no loops or multiple edges. A graph is nonsimple if it has loops or multiple edges.<\/p>\n<p>A graph is connected if there is a path between any two vertices in the graph. A graph is disconnected if there is no path between any two vertices in the graph.<\/p>\n<p>A graph is simple if it has no loops or multiple edges. A graph is nonsimple if it has loops or multiple edges.<\/p>\n<p>A graph is connected if there is a path between any two vertices in the graph. A graph is disconnected if there is no path between any two vertices in the graph.<\/p>\n<p>A graph is simple if it has no loops or multiple edges. A graph is nonsimple if it has loops or multiple edges.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Difference_Between_Circuit_and_Cycle_in_Graph_Theory\"><\/span>Difference Between Circuit and Cycle in Graph Theory<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A circuit is a path in a graph that starts and ends at the same vertex. A cycle is a path in a graph that starts and ends at different vertices.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Graph_Theory_and_Application_Question_Bank\"><\/span>Graph Theory and Application Question Bank<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. What is a graph?<\/p>\n<p>A graph is a collection of points, called vertices, and the lines connecting them, called edges.<\/p>\n<p>2. What is a connected graph?<\/p>\n<p>A connected graph is a graph in which there exists a path between any two vertices.<\/p>\n<p>3. What is a disconnected graph?<\/p>\n<p>A disconnected graph is a graph in which there is no path between any two vertices.<\/p>\n<p>4. What is a simple graph?<\/p>\n<p>A simple graph is a graph in which each edge connects two different vertices.<\/p>\n<p>5. What is a multigraph?<\/p>\n<p>A multigraph is a graph in which two or more edges may connect the same two vertices.<\/p>\n<p>6. What is a graph isomorphism?<\/p>\n<p>A graph isomorphism is a relationship between two graphs in which one can be transformed into the other by a sequence of graph transformations that preserves the edge relationships.<\/p>\n<p>7. What is a degree sequence?<\/p>\n<p>A degree sequence is a list of the degrees of the vertices in a graph, listed in ascending order.<\/p>\n<p>8. What is a degree?<\/p>\n<p>The degree of a vertex is the number of edges incident to that vertex.<\/p>\n<p>9. What is a path?<\/p>\n<p>A path is a sequence of connected edges between two vertices.<\/p>\n<p>10. What is a cycle?<\/p>\n<p>A cycle is a path that includes<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Graph Theory Graph theory is the study of graphs and their properties. A graph consists of a set [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Graph Theory","_yoast_wpseo_title":"Graph Theory \u2013 Introduction, Explanation, Terminologies, and FAQs","_yoast_wpseo_metadesc":"Learn about graph theory topic of maths in details explained by subject experts on infinitylearn.com. 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