A self-complementary digraph is a directed graph that is isomorphic to its graph complement, where
the complement has the same vertices and exactly the arcs absent from the original
digraph.
Read (1963) determined the number of self-complementary graphs and digraphs. Harary and Palmer (1973, p. 260) list the enumeration
of labeled self-complementary graphs and digraphs as a graphical enumeration problem.
Harary, F. and Palmer, E. M. "A Survey of Graphical Enumeration Problems." In A Survey of Combinatorial Theory (Ed. J. N. Srivastava).
Amsterdam, Netherlands: North-Holland, pp. 259-275, 1973.Read,
R. C. "On the Number of Self-Complementary Graphs and Digraphs." J.
London Math. Soc.38, 99-104, 1963.
