Abstract:A cyclic subgroup graph of a group is a graph whose vertices are cyclic subgroups of the group, and two distinct vertices are adjacent if one is a maximal subgroup of the other. In this paper, we examine several graph-theoretic properties of cyclic subgroup graphs, including bipartiteness, regularity, girth, diameter, and vertex degrees. We also classify all groups whose cyclic subgroup graphs are connected, complete, star graphs, trees, or paths. Further, we examine the cyclic subgroup graph for specific families of groups such as cyclic, dihedral, dicyclic, generalized quaternion, minimal non-cyclic and nilpotent groups. We also discuss the relationship of cyclic subgroup graph with the power graph and the enhanced power graph. Additionally, we give a relationship between a cyclic subgroup graph and a poset.
From: Satyanarayana Reddy Arikatla [view email]
[v1]
Fri, 20 Sep 2024 12:47:16 UTC (13 KB)
[v2]
Wed, 16 Sep 2026 09:06:19 UTC (28 KB)
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