On arc-transitive Cayley digraphs of out-valency 3

Abstract

Abstract 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 = 〈 S S − 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 A 47 . 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.