Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 3 2026 07 01 The undirected power graph on the conjugacy classes of a finite group 321 324 5679 10.22060/ajmc.2025.23715.1293 EN Sajjad Mahmood Robati Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Journal Article 2024 11 28 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. https://ajmc.aut.ac.ir/article_5679_166cee72e93a992007a89b39eb29628b.pdf