Commuting conjugacy classes graph of the generalized dihedral and dicyclic groups

Document Type : Research Paper

Author

Department of Mathematics, Swadkoh Branch, Islamic Azad University, Swadkoh, Iran

Abstract

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.

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Volume 7, Issue 4 - Serial Number 4
December 2022
Pages 33-42
  • Receive Date: 13 December 2022
  • Revise Date: 11 March 2023
  • Accept Date: 12 March 2023
  • Publish Date: 20 February 2023