Journal article

Classification of tetravalent 2-transitive nonnormal Cayley graphs of finite simple groups

XG Fang, J Wang, S Zhou

Bulletin of the Australian Mathematical Society | Published : 2020

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,..

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