On G-arc-regular dihedrants and regular dihedral maps

Abstract

A graph Γ is said to be G-arc-regular if a subgroup G ≤ Aut(Γ ) acts regularly on the arcs of Γ . In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D2n of order 2n whose cyclic subgroup Cn ≤ D2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D2n, n odd, are classified.