Document Type : Research Paper

**Authors**

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran

10.29252/as.2020.1839

**Abstract**

Suppose that $G$ is a finite non-abelian group. Define the graph $\Gamma(G)$ with the non-central conjugacy classes of $G$ as vertex set and two distinct vertices $A$ and $B$ are adjacent if and only if there are $x \in A$ and $y \in B$ such that $xy = yx$. The graph $\Gamma(G)$ is called the commuting conjugacy class graph of $G$ and introduced by Mohammadian et al. in [A. Mohammadian, A. Erfanian, M. Farrokhi D. G. and B. Wilkens, Triangle-free commuting conjugacy class graphs, {J. Group Theory} {19} (3) (2016) 1049--1061]. In this paper, the graph structure of the commuting conjugacy class graph of nilpotent groups of order $n$ are obtained in which $n$ is not divisible by $p^5$, for every prime factor $p$ of $n$.

**Keywords**

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Summer and Autumn 2020

Pages 135-145