On the number of edges of cyclic subgroup graphs of finite groups

DOI10.1007/S00013-023-01846-1arXiv2302.05784MaRDI QIDQ6426186

Publication date: 11 February 2023

Abstract: In this note, we show that among finite nilpotent groups of a given order or finite groups of a given odd order, the cyclic group of that order has the minimum number of edges in its cyclic subgroup graph. We also conjecture that this holds for arbitrary finite groups.

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Finite nilpotent groups, (p)-groups (20D15) Vertex degrees (05C07)

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