On oriented $m$-semiregular representations of finite groups about valency two

Jia-Li Du, Young Soo Kwon, Da-Wei Yang

Given a group $G$, an {\em $m$-Cayley digraph $\G$ over $G$} is a digraph that has a group of automorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$ orbits…