Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$

Abstract

‎Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a graph with non-central conjugacy classes of $G$ as its vertex set. Two vertices $L$ and $K$ in $\Gamma(G)$ are adjacent if there are $a \in L$ and $b \in K$ such that $ab = ba$. This graph is called the commuting conjugacy class graph of $G$. The purpose of this paper is to compute the commuting conjugacy class graph of the finite $2-$groups $G_n(m)$ and $G[n]$.

Keywords

• commuting conjugacy class graph‎
• ‎conjugacy class‎
• ‎center