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

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) ≤ S6.