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

	The undirected power graph on the conjugacy classes of a finite group
AUT Journal of Mathematics and Computing
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از 28 بهمن 1403
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2025.23715.1293
نویسنده
Sajjad Mahmood Robati^*
Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
چکیده
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.
کلیدواژه‌ها
Conjugacy classes؛ $2$-Connected graph؛ Bipartite graph؛ Finite group
آمار تعداد مشاهده مقاله: 228