AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

The undirected power graph on the conjugacy classes of a finite group

Document Type : Original Article

Author
Sajjad Mahmood Robati
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
10.22060/ajmc.2025.23715.1293
Abstract
Let $G$ be a finite group. The undirected power graph on the conjugacy classes of $G$ is the simple graph $\mathcal{P_C}(G)$ whose vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent if one is a subset of a power of the other. In this paper, we show that the graph $\mathcal{P_C}(G)$ is $2$-connected whenever either $|\pi(G)|>1$ or ${\rm Z}(G)$ is cyclic. Moreover, we classify finite groups $G$ whose associated graph $\mathcal{P_C}(G)-\{e\}$ are bipartite.
Keywords
Conjugacy classes
$2$-Connected graph
Bipartite graph
Finite group
Subjects
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AUT Journal of Mathematics and Computing
Volume 7, Issue 3
Summer 2026
Pages 321-324