On Automorphism Groups of Symmetric Cayley Graphs of Finite Simple Groups with Valency Six

Abstract

In this paper we investigate the full automorphism groups of six-valent symmetric Cayley graphs Γ = Cay (G,S) for finite non-abelian simple groups G. We prove that for most finite non-abelian simple groups G, if Γ contains no cycle of length 4, then Aut Γ = G · Aut (G,S), where Aut (G,S) ≤ S 6.