A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS

Abstract

The commuting graph of a group is a graph with vertexes set of a subset of a group and two<br /> element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting<br /> graph of a conjugacy class in the symmetric groups. The clique number, coloring number,<br /> independent number, and diameter of these graphs are also computed.