We prove that, with very few exceptions, every graph of order n, n = 0, 1 (mod 4) and size a t most n 1, is contained in a self-complementary graph of order n. We study a similar problem for digraphs. Throughout the paper, G and D will denote a finite graph and a finite digraph, respectively, without loops or multiple edges, with vertex-sets V(G) and V ( D ) , and edge-sets E(G) and E(D); define r (G) = IE(G)I, e(D) = (E(D)I. An edge of G joining x and y is denoted by xy, an edge of D from i to… CONTINUE READING