Cubic s-arc-transitive bi-Cayley graphs

Abstract

A bipartite graph Γ is a bi-Cayley graph over a group H if $H⩽\mathrm{Aut}\Gamma$ acts regularly on each part of Γ. A bi-Cayley graph Γ over a group H is said to be core-free if H is core-free in the bipartition-preserving subgroup of X for $X⩽\mathrm{Aut}\Gamma$. In this paper, a classification is given for cubic core-free s-arc-transitive bi-Cayley graphs.