Abstract:For a finite group $G$, we say that a Cayley graph $\Gamma$ on $G$ is a most rigid representation (MRR) of $G$ if its full automorphism group has the smallest possible order among all Cayley graphs on $G$, and say that $\Gamma$ is stable if every automorphism of $\Gamma\times K_2$ comes from $\mathrm{Aut}(\Gamma)\times\Aut(K_2)$. Although the study of stability has attracted significant attention, particularly regarding Cayley graphs on abelian groups, a complete classification is currently out of reach even for Cayley graphs on cyclic groups. In this paper, we prove that almost all Cayley graphs on finite abelian groups are stable MRRs. This strengthens the main result of Dobson, Spiga and Verret [Combinatorica, 36 (2016), no.~4, 371--393], which states that almost all Cayley graphs on finite abelian groups are MRRs.
From: Binzhou Xia [view email]
[v1]
Wed, 28 Jan 2026 03:29:56 UTC (26 KB)
[v2]
Thu, 17 Sep 2026 02:54:39 UTC (29 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。