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On the Diameter of Undirected Cayley Graphs of Finite Abelian Groups (2406.04045v1)
Published 6 Jun 2024 in math.CO, math.GR, and math.NT
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 $\Gamma(G,A)$ 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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