On cubic s-arc transitive Cayley graphs of finite simple groups

For a positive integer s, a graph Γ is called s-arc transitive if its full automorphism group AutΓ acts transitively on the set of s-arcs of Γ . Given a group G and a subset S of G with S = S−1 and 1 / ∈ S, let Γ = Cay(G, S) be the Cayley graph of G with respect to S and G R the set of right translations of G on G. Then G R forms a regular subgroup of AutΓ . A Cayley graph Γ = Cay(G, S) is called normal if G R is normal in AutΓ . In this paper we investigate connected cubic s-arc transitive Cayley graphs Γ of finite non-Abelian simple groups. Based on Li’s work (Ph.D. Thesis (1996)), we prove that either Γ is normal with s ≤ 2 or G = A47 with s = 5 and AutΓ ∼= A48. Further, a connected 5-arc transitive cubic Cayley graph of A47 is constructed. © 2004 Elsevier Ltd. All rights reserved.