Digraph Representations of 2-closed Permutation Groups with a Normal Regular Cyclic Subgroup

Abstract

In this paper, we classify 2-closed (in Wielandt's sense) permutation groups which contain a normal  regular cyclic subgroup and prove that for each such group $G$, there exists a circulant $\Gamma$ such that $\mathrm{Aut} (\Gamma)=G$.