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25 Oct 2001 Brief Discussion of Graph Theory. A graph is defined a collection of vertices (or nodes) and edges connecting them. Formally, , where is a set of unordered pairs from . Figure 1 shows an example graph: edge but edge . 11 Jan 2007 •complete subgraph of a graph: part of a graph in which all •cliques: maximal complete subgraphs (not subsumed by any algorithms (cf.3 Sep 2017 We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of From the lesson Then we will see how cliques and independent sets are related in graphs. 23 Feb 2015 22 Jan 2019 Abstract—Since its first use by Euler on the seven bridges of. Konigsberg problem, graph theory has shown excellent abilities in solving and Graph Theory Tutorial - Learn Graph Theory in simple and easy steps starting from Introduction, Fundamentals, Basic Properties, Types Of Graphs, Trees, A clique of a graph is a complete subgraph of , and the clique of largest possible size is referred to as a maximum clique. A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. Definitions. A clique, C, in an undirected graph G = (V, E) is a subset of the vertices, C ? V, such that every two distinct vertices are adjacent. This is equivalent to the condition that the induced subgraph of G induced by C is a complete graph. 4 Jan 2018 That is, every two distinct vertices in C are connected by a distinct edge of the graph. This means different edges, not the same. So, on a clique