Consistent Cycles in $1\over2$-Arc-Transitive Graphs

Abstract

A directed cycle $C$ of a graph is called $1\over k$-consistent if there exists an automorphism of the graph which acts as a $k$-step rotation of $C$. These cycles have previously been considered by several authors in the context of arc-transitive graphs. In this paper we extend these results to the case of graphs which are vertex-transitive, edge-transitive but not arc-transitive.