Self-Complementary Vertex-Transitive Graphs need not be Cayley Graphs

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs, To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.