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

AbstractFor 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 GR the set of right translations of G on G. Then GR forms a regular subgroup of AutΓ. A Cayley graph Γ=Cay(G,S) is called normal if GR 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