Tetravalent 2-arc-transitive Cayley graphs on non-abelian simple groups

2017/01/04 by Jia‐Li Du, Du, Jia-Li, Yan‐Quan Feng +1 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1701.01180

openalex publication_date 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A graph Gamma is said to be 2-arc-transitive if its full automorphism group Aut(Γ) has a single orbit on ordered paths of length 2, and for G≤ Aut(Γ), Γis G-regular if G is regular on the vertex set of Γ. Let G be a finite non-abelian simple group and let Γbe a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li and Xu proved that either G\unlhd \Aut(Γ) or G is one of 22 possible candidates. In this paper, the number of candidates is reduced to 7, and for each candidate G, it is shown that \Aut(Γ) has a normal arc-transitive non-abelian simple subgroup T such that G≤ T and the pair (G,T) is explicitly given

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