Complete graphs are simple graphs such that any two vertices are joined by an edge. As an unlabelled graph, a complete graph is simply determined

by the number n of its vertices. It is generally denoted by K_n (see Figure 1.1for the case n = 5). The number of edges m of K_n is equal to the binomial

coefficient ,that is:

                                                           Figure 1.1. The complete graph K₅

Note. More generally, we can write for any simple graph with n vertices and m edges (indicate why):

Graph Theory  and Applications ,Jean-Claude Fournier, WILEY, page(28)