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.
Mahmood Robati, S. (2025). The undirected power graph on the conjugacy classes of a finite group. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2025.23715.1293
MLA
Mahmood Robati, S. . "The undirected power graph on the conjugacy classes of a finite group", AUT Journal of Mathematics and Computing, , , 2025, -. doi: 10.22060/ajmc.2025.23715.1293
HARVARD
Mahmood Robati, S. (2025). 'The undirected power graph on the conjugacy classes of a finite group', AUT Journal of Mathematics and Computing, (), pp. -. doi: 10.22060/ajmc.2025.23715.1293
CHICAGO
S. Mahmood Robati, "The undirected power graph on the conjugacy classes of a finite group," AUT Journal of Mathematics and Computing, (2025): -, doi: 10.22060/ajmc.2025.23715.1293
VANCOUVER
Mahmood Robati, S. The undirected power graph on the conjugacy classes of a finite group. AUT Journal of Mathematics and Computing, 2025; (): -. doi: 10.22060/ajmc.2025.23715.1293
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