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

For a positive integer s, a graph Gamma is called s-arc transitive if its full automorphism group AutGamma acts transitively on the set of s-arcs of Gamma. Given a group G and a subset S of G with S = S-1 and 1 is not an element of S, let Gamma = 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 GR forms a regular subgroup of AutGamma. A Cayley graph Gamma = Cay(G, S) is called normal if G(R) is normal in AutGamma. In this paper we investigate connected cubic s-arc transitive Cayley graphs Gamma of finite non-Abelian simple groups. Based on Li's work (Ph.D. Thesis (1996)), we prove that either Gamma is normal with s less than or equal to 2 or G = A(47) with s = 5 and AutGamma congruent to A(48). Further, a connected 5-arc transitive cubic Cayley graph of A47 is constructed. (C) 2004 Elsevier Ltd. All rights reserved.