Self-complementary and self-converse oriented graphs

AbstractDe Bruijn [I] applied his genoralization of PÓlya's fundamental theorem to provide an outline of a general method for enumerating self-complementary structures. This was used by Read [8] to carry out in detail the enumeration of self-complementary graphs and digraphs. Suitable modifications of the same scheme gave Harary and Palmer [4], [5] the basic clue for their enumeration of self-converse digraphs. In this paper we extend these results to obtain the formula for the number of self-complementary oriented graphs on n points and the generating function for self-converse oriented graphs in terns of the number of lines