Seyed H. Jafari - Department of Mathematics, Shahrood University of Technology, P.O. Box ۳۶۱۹۹۹۵۱۶۱-۳۱۶, Shahrood, Iran.

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

symmetric group, automorphim group, commuting graph