Commuting Co.njugacy Class Graph of Finite CA-Groups

Abstract

Let  G be a finite nonabelian group. The commuting conjugacy class graph  Γ(G) is a simple graph with the noncentral conjugacy classes of G as its vertex set and two distinct vertices X and Y in Γ(G) are adjacent if and only if there are  x∈X and y∈Y with this property that xy=yx. The aim of this paper is to obtain the structure of the commuting conjugacy class graph of  finite CA-groups. It is proved that this graph is a union of some complete graphs. The commuting conjugacy class graph of certain groups are also  computed.