The base size of vertex-transitive cubic graphs

Abstract

We prove that if $\hat{I}“$ is a finite connected vertex-transitive cubic graph, then either $|V\hat{I}“|\le 90$, or $\hat{I}“$ is a split Praeger--Xu graph, or there exist two vertices $\hat{I}\pm$ and ${\hat{I}}^2$ such that the identity is the only automorphism of $\hat{I}“$ fixing both $\hat{I}\pm$ and ${\hat{I}}^2$.

37 pages