May 28, 2024Open Access

The commuting graphs of certain cyclic-by-abelian groups

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Abstract

Let G be a finite, non-abelian group of the form G = A N, where A G is abelian, and N G is cyclic. We prove that the commuting graph (G) of G is either a connected graph of diameter at most four, or the disjoint union of several complete graphs. These results apply to all finite metacyclic groups, and groups of square-free order in particular.

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Timo Velten (Tue,) studied this question.

synapsesocial.com/papers/68e68232b6db64358760b845 https://doi.org/https://doi.org/10.48550/arxiv.2405.18103

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