Symmetric cubic graphs with non-solvable automorphism groups

Abstract

A cubic graph Γ is called G-symmetric if a group G of automorphisms of Γ acts transitively on the arcs of Γ, and G-basic if it is G-symmetric and G has no non-trivial normal subgroups with more than two orbits on the vertex set of Γ. We say the graph Γ is basic if it is G-basic for all arc-transitive subgroups G of Aut(Γ). All basic symmetric cubic graphs with solvable automorphism groups have been classified in Feng et al. (2015) [12]. In this paper, a characterization of basic symmetric cubic graphs with non-solvable automorphism groups is given.