CLASSIFICATION of TETRAVALENT 2-TRANSITIVE NONNORMAL CAYLEY GRAPHS of FINITE SIMPLE GROUPS

Abstract

A graph Γ is called (G, s)-arc-transitive if G ≤ Aut(Γ) is transitive on the set of vertices of Γ and the set of s-arcs of Γ, where for an integer s ≤ 1 an s-arc of Γ is a sequence of s + 1 vertices (v0, v1, ⋯, vs) of Γ such that vi-1 and vi are adjacent for 1 ≤ i ≤ s and vi-1 ≠ vi+1 for 1 ≤ i ≤ s - 1. A graph Γ is called 2-transitive if it is (Aut(Γ), 2)-arc-transitive but not (Aut(Γ), 3)-arc-transitive. A Cayley graph Γ of a group G is called normal if G is normal in Aut(Γ) and nonnormal otherwise. Fang et al. ['On edge transitive Cayley graphs of valency four', European J. Combin. 25 (2004), 1103-1116] proved that if Γ is a tetravalent 2-transitive Cayley graph of a finite simple group G,..