Year: 2025
Type: preprint
Abstract: A pair of graphs $(Γ,Σ)$ is called unstable if their direct product $Γ\timesΣ$ admits automorphisms not from $\mathrm{Aut}(Γ)\times\mathrm{Aut}(Σ)$, and such automorphisms are said to be unexpected. The stability of a graph $Γ$ refers to that of $(Γ,K_2)$. While the stability of individual graphs has been relatively well studied, much less is known for graph pairs. In this paper, we propose a conjecture that provides the best possible reduction of the stability of a graph pair to the stability of a single graph. We prove one direction of this conjecture and establish partial results for the converse. This enables the determination of the stability of a broad class of graph pairs, with complete results when one factor is a cycle.
Source: arXiv (Cornell University)
Authors: Wang, Xiaomeng, Qin, Yan-Li, Xia, Binzhou
Institution: Lanzhou University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1744826215, G3330263845, G7641881801
OpenAlex ID: W7084088927
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