Symmetric graphs of prime valency with a transitive simple group

2021/03/31 by Jing Jian Li, Li, Jing Jian, Zai Ping Lu +1
Computer Science · Mathematics · #05C25 #20B25 #20D40 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2103.16870

openalex publication_date 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A graph \Ga=(V,E) is called a Cayley graph of some group T if the automorphism group \Aut(\Ga) contains a subgroup T which acts on regularly on V. If the subgroup T is normal in \Aut(\Ga) then \Ga is called a normal Cayley graph of T. Let r be an odd prime. Fang et al. \citeFMW proved that, with a finite number of exceptions for finite simple group T, every connected symmetric Cayley graph of T of valency r is normal. In this paper, employing maximal factorizations of finite almost simple groups, we work out a possible list of those exceptions for T.

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