Commuting Conjugacy Class Graph of Finite CA-Groups

Document Type : Original Article


Department of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.


Let  $G$ be a finite nonabelian group. The commuting conjugacy class graph  $\Gamma(G)$ is a simple graph with the noncentral conjugacy classes of $G$ as its vertex set and two distinct vertices $X$ and $Y$ in $\Gamma(G)$ are adjacent if and only if there are  $x \in X$ and $y \in Y$ 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.