On weakly symmetric graphs of order twice a prime square

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 arc-transitive. In 1987, Cheng and Oxley determined all weakly symmetric graphs of order twice a prime and showed that these graphs are arc-transitive, too. In this paper, a characterization of weakly symmetric graphs of order twice a prime square is given, and it shows that these graphs are also arc-transitive.