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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 تاریخ 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 | ||
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آمار تعداد مشاهده مقاله: 29 |
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