University of Isfahan Mathematics and Society 2345-6493 7 4 2023 02 20 Commuting conjugacy classes graph of the generalized dihedral and dicyclic groups Commuting conjugacy classes graph of the generalized dihedral and dicyclic groups 33 42 27398 10.22108/msci.2023.136084.1549 FA Mohammadali Salahshour Department of Mathematics, Swadkoh Branch, Islamic Azad University, Swadkoh, Iran Journal Article 2022 12 13 Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a simple graph with the non-central conjugacy classes of $G$ as its vertex set. Two different non-central conjugacy classes $A$ and $B$ are assumed to be adjacent if and only if there are elements $a,b \in G$ such that $a \in A$, $b \in B$ and $ab = ba$. This graph is called the commuting conjugacy class graph of G. In this paper, the structure of the commuting conjugacy class graph of the generalized dihedral group $D_{(m,n)}$ and the generalized dicyclic group $Dic (A, y, x)$ are completely determined. Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a simple graph with the non-central conjugacy classes of $G$ as its vertex set. Two different non-central conjugacy classes $A$ and $B$ are assumed to be adjacent if and only if there are elements $a,b \in G$ such that $a \in A$, $b \in B$ and $ab = ba$. This graph is called the commuting conjugacy class graph of G. In this paper, the structure of the commuting conjugacy class graph of the generalized dihedral group $D_{(m,n)}$ and the generalized dicyclic group $Dic (A, y, x)$ are completely determined. https://math-sci.ui.ac.ir/article_27398_1f2e89c30694986a290c3e5e84aad028.pdf