On arc-transitive Cayley digraphs of out-valency 3.

In this paper, based on the calculation using GAP, we give a classification result on arc-transitive Cayley digraphs of finite simple groups. Let G be a finite simple group and S⊂G∖{1} with |S|=3, S≠S−1 and G=〈SS−1〉. If the Cayley digraph Γ=Cay(G,S) is arc-transitive, then Γ is either normal or isomorphic to one of 382 Cayley digraphs of the alternating group A47. Further, we consider the underlying graphs and standard double covers of these 382 Cayley digraphs, and then we get 172 (non-isomorphic) half-transitive Cayley graphs of valency 6, and 144 semisymmetric cubic graphs.