Tetravalent 2-arc-transitive Cayley graphs on non-abelian simple groups

Let G be a finite non-abelian simple group and let be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the full automorphism group of , or G is one of up to 22 exceptional candidates. In this paper, the number of exceptions is reduced to 7, and for each one, it is shown that has a normal arc-transitive non-abelian simple subgroup T such that and the pair (G, T) is explicitly given. Furthermore, there exists a G-regular -arc-transitive graph for each of the 7 pairs (G, T).