Document Type: Original Manuscript


Department of Mathematics, Shahrood University of Technology, P.O. Box 3619995161-316, 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.