Graph Theory

In this chapter, the authors show how MATLAB can be used to construct the cycle index of S_n acting on the set E of all possible edges of an undirected graph with n vertices, and the resulting pattern inventory. They also show how Maple can be used to construct the cycle index of S_n acting on the set E of all possible edges of an undirected graph with n vertices, and the resulting pattern inventory. The authors deal with the notion of a partition of a positive integer. They describe devise a method for counting the number of nonequivalent undirected graphs with n vertices for a positive integer n, with two graphs equivalent if there is a bijection on their vertices that induces a bijection on their edges.