The clique number of the intersection graph of some cyclic groups

Beheshtipour, Arezoo; Jafarian Amiri, Seyyed Majid

doi:10.22108/ijgt.2025.140733.1892

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	The clique number of the intersection graph of some cyclic groups
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 21 اسفند 1403 اصل مقاله (414.49 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.140733.1892
نویسندگان
Arezoo Beheshtipour؛ Seyyed Majid Jafarian Amiri^*
Department of Mathematics, University of Zanjan, P.O. Box 45371-38791, Zanjan, Iran
چکیده
For a nontrivial finite group $G$, the intersection graph $\Gamma(G)$ of $G$ is a simple undirected graph whose vertices are the nontrivial proper subgroups of $G$ and two vertices are joined by an edge if and only if they have a nontrivial intersection. In this paper, we obtain the clique number of the intersection graph of cyclic groups whose orders have four prime divisors. Moreover we find the clique number of the intersection graph of cyclic groups of order $n$ such that all powers of prime divisors of $n$ are equal. As a special case, we find the clique number of this graph for the cyclic groups of the square-free orders.
کلیدواژه‌ها
Finite group؛ intersection graph؛ clique number؛ cyclic group

مراجع
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The clique number of the intersection graph of some cyclic groups