On weakly symmetric graphs of order twice a prime

Abstract

A graph is weakly symmetric if its automorphism group is both vertex-transitive and edge-transitive. In 1971, Chao characterized all weakly symmetric graphs of prime order and showed that such graphs are also transitive on directed edges. In this paper we determine all weakly symmetric graphs of order twice a prime and show that these graphs too are directed-edge transitive. © 1987