The clique number of the intersection graph of some cyclic groups

Beheshtipour, Arezoo; Jafarian Amiri, Seyyed Majid

doi:10.22108/ijgt.2025.140733.1892

تعداد نشریات	43
تعداد شماره‌ها	1,829
تعداد مقالات	14,864
تعداد مشاهده مقاله	40,730,321
تعداد دریافت فایل اصل مقاله	15,807,216

	The clique number of the intersection graph of some cyclic groups
International Journal of Group Theory
دوره 15، شماره 1، خرداد 2026، صفحه 9-16 اصل مقاله (426.32 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
[1] H. Ahmadi and B. Taeri, Planarity of the intersection graph of subgroups of a finite groups, J. Algebra Appl., 15 no. 3 (2016) 19 pp. [2] A. Beheshtipour and S. M. Jafarian Amiri, The clique number of the intersection graph of a finite group, Bull. Iran. Math. Soc., 49 no. 5 (2023) 16 pp. [3] A. Beheshtipour and S. M. Jafarian Amiri, The clique number of the intersection graph of a cyclic group of order with at most three prime factors, Journal of Mathematics and Society, 8 no. 4 (2023) 21–25. [4] A. Beheshtipour and S. M. Jafarian Amiri, The clique number of the intersection graph of PSL(2, 7), submitted. [5] M. H. Bien and D. H. Viet, Intersection graphs of general linear groups, J. Algebra Appl., 20no. 3 (2021) 14 pp. [6] J. Bosak, The graphs of semigroups, Theory of Graphs and its Applications (Proc. Sympos. Smolenice, 1963), Publ. House Czech. Acad. Sci., Prague, 1964 119–125. [7] P. J. Cameron, Graphs defined on groups, Int. J. Group Theory, 11 (2022) 53–107. [8] B. Csákány and G. Pollák, The graph of subgroups of a finite group, Czech. Math. J., 19 (1969) 241–247. [9] Saul D. Freedman, The intersection graph of a finite simple group has diameter at most 5, Arch. Math. (Basel), 117 no. 1 (2021) 1–7. [10] M. Herzog, P. Longobardi and M. Maj, On a graph related to maximal subgroups of a group, Bull. Austral. Math. Soc., 81 (2010) 317–328. [11] S. Kayacan, Connectivity of intersection graphs of finite groups, Comm. Algebra, 46 no. 4 (2018) 1492–1505. [12] S. Kayacan and S. E. Yaraneri, Finite groups whose intersection graphs are planar, J. Kor. Math. Soc. 52 no. 1 (2015) 81–96. [13] D. J. S. Robinson, A course in the theory of groups, Springer-Verlag New York, 1996. [14] H. Shahsavari and B. Khosravi, Characterization by intersection graph of some families of finite simple groups, Publ. Math. Debrecen, 102 no. 1-2 (2023) 45–60. [15] H. Shahsavari and B. Khosravi, Characterization of some families of simple groups by their intersection graphs, Comm. Algebra, 48 (2020) 1266–1280. [16] H. Shahsavari and B. Khosravi, On the intersection graph of a finite group, Czech. Math. J., 67no. 4 (2017) 1145–1153. [17] R. Shen, Intersection graphs of subgroups of finite groups, Czech. Math. J., 60 (2010) 945–950. [18] H. Su and L. Zhu, Thickness of the subgroup intersection graph of a finite group, AIMS Math., 6 no. 3 (2021) 2590–2606. [19] B. Zelinka, Intersection graphs of finite abelian groups, Czech. Math. J., 25 (1975) 171–174.
آمار تعداد مشاهده مقاله: 189 تعداد دریافت فایل اصل مقاله: 146

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

The clique number of the intersection graph of some cyclic groups