The base size of vertex-transitive cubic graphs

Abstract

We prove that if $Γ$ is a finite connected vertex-transitive cubic graph, then either $|VΓ| \le 90$, or $Γ$ is a split Praeger--Xu graph, or there exist two vertices $α$ and $β$ such that the identity is the only automorphism of $Γ$ fixing both $α$ and $β$.