1-Regular Cayley Graphs of Valency 7

Abstract

A graph Γ is called 1-regular if AutΓ acts regularly on its arcs. In this paper, a classification of 1-regular Cayley graphs of valency 7 is given; in particular, it is proved that there is only one core-free graph up to isomorphism.2010 Mathematics subject classification: primary 05C25.