Arc-transitive Cayley graphs on non-ableian simple groups with soluble vertex stabilizers and valency seven

2017/07/31 by Jiangmin Pan, Pan, Jiangmin, Fu‐Gang Yin +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1707.09785

openalex publication_date 2017/07/31 · openalex created_date 2017/08/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we study arc-transitive Cayley graphs on non-abelian simple groups with soluble stabilizers and valency seven. Let \Ga be such a Cayley graph on a non-abelian simple group T. It is proved that either \Ga is a normal Cayley graph or \Ga is S-arc-transitive, with (S,T)=(\A_n,\A_n-1) and n=7,21,63 or 84; and, for each of these four values of n, there really exists arc-transitive 7-valent non-normal Cayley graphs on \A_n-1 and specific examples are constructed.

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