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arXiv · 2406.04045

On the Diameter of Undirected Cayley Graphs of Finite Abelian Groups

Bela Bajnok·W. Kyle Beatty
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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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Bela Bajnok, W. Kyle Beatty. 2024-06-06. On the Diameter of Undirected Cayley Graphs of Finite Abelian Groups. https://doi.org/10.2140/cnt.2025.14.1

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