Tetravalent half‐arc‐transitive bi‐p‐metacirculants

Abstract

AbstractA graph is half‐arc‐transitive if its full automorphism group acts transitively on its vertex set and edge set, but not arc set. A graph is said to be a bi‐Cayley graph over a group if it admits as a group of automorphisms acting semiregularly and with two orbits on the vertex set. In this paper, a classification is given of tetravalent half‐arc‐transitive bi‐Cayley graphs over metacyclic ‐groups for each odd prime , and this is then used to give a classification of tetravalent half‐arc‐transitive graphs of order twice a prime cube.