The commuting graphs of certain cyclic-by-abelian groups

2024/05/28 by Timo Velten, Velten, Timo
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.18103

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite, non-abelian group of the form G = A N, where A ≤ G is abelian, and N \trianglelefteq G is cyclic. We prove that the commuting graph Γ(G) of G is either a connected graph of diameter at most four, or the disjoint union of |G'| + 1 complete graphs. These results apply to all finite metacyclic groups, and to groups of square-free order in particular.

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