An alternative enumeration of self-complementary graphs

Abstract

Let e(n), o(n), sc(n) be the number of unlabelled graphs of order n with an even number of edges, the number of those with an odd number of edges, and the number of unlabelled self-complementary graphs of order, n, respectively. In 2001, Gordon F. Royle conjectured the equality sc(n) = e(n) - o(n). This paper shows that this conjecture is true.