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. (e5679). AUT Journal of Mathematics and Computing, (), e5679 doi: 10.22060/ajmc.2025.23715.1293
MLA
Mahmood Robati,S. . "The undirected power graph on the conjugacy classes of a finite group" .e5679 , AUT Journal of Mathematics and Computing, , , 2025, e5679. 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, (), e5679. 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): e5679, doi: 10.22060/ajmc.2025.23715.1293
VANCOUVER
Mahmood Robati S. The undirected power graph on the conjugacy classes of a finite group. AUT J Math Comput, 2025; (): e5679. doi: 10.22060/ajmc.2025.23715.1293
