Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47886120200101Commuting Conjugacy Class Graph of Finite CA-Groups1081189717710.22034/kjm.2019.97177ENMohammad AliSalahshourDepartment of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.Ali RezaAshrafiDepartment of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.Journal Article20190215Let $G$ 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.http://www.kjm-math.org/article_97177_3bc76fe226764a53f2b1071b15cca234.pdf