On the automorphism groups of Cayley graphs of finite simple groups

Let G be a finite nonabelian simple group and let Gamma be a connected undirected Cayley graph for G. The possible structures for the full automorphism group AutGamma are specified. Then, for certain finite simple groups G, a sufficient condition is given under which G is a normal subgroup of AutGamma. Finally, as an application of these results, several new half-transitive graphs are constructed. Some of these involve the sporadic simple groups G J(1), J(4), Ly and BM, while others fall into two infinite families and involve the Ree simple groups and alternating groups. The two infinite families contain examples of half-transitive graphs of arbitrarily large valency.