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On the diameter of undirected Cayley graphs of finite abelian groups

Béla Bajnok and W. Kyle Beatty
Vol. 14 (2025), No. 1, 1–12
DOI: 10.2140/cnt.2025.14.1
Abstract

Let s be a positive integer. Our goal is to find all finite abelian groups G that contain a 2-subset A for which the undirected Cayley graph Γ(G,A) has diameter at most s. We provide a complete answer when G is cyclic, and a conjecture and some partial answers when G is noncyclic.

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Keywords
abelian group, Cayley graph, diameter, sumset, signed sumset
Mathematical Subject Classification
Primary: 11B13
Secondary: 05B10, 05C35, 11B75, 11P70, 20K01
Milestones
Received: 4 April 2024
Revised: 26 October 2024
Accepted: 12 November 2024
Published: 10 December 2024
Authors
Béla Bajnok
Department of Mathematics
Gettysburg College
Gettysburg, PA
United States
W. Kyle Beatty
Department of Applied Mathematics and Statistics
Johns Hopkins University
Baltimore, MD
United States
© 2025 MSP (Mathematical Sciences Publishers).