A graph G is self complementary if it is isomorphic to its complement G. In this paper we define bipartite self-complementary graphs, and show how they can be used to understand the structure of self-complementary graphs. For G a selfcomplementary graph of odd order, we describe a decomposition of G into edge disjoint subgraphs, one of which is a bipartite self-complementary graph of order |G|−...

A graph is self-complementary if it is isomorphic to its complement. In this paper we prove that every forest of order 4p and size less than 3p is a subgraph of a self-complementary graph of order 4p with a cyclic self-complementary permutation. We also discuss some generalization of the main result.

A graph X is called almost self-complementary with respect to a perfect matching I in the complement Xc if it is isomorphic to the graph obtained from Xc by removing the edges of I. In this paper we investigate the relationship between self-complementary two-graphs and double covers over complete graphs that are almost self-complementary with respect to their set of fibres. In particular, we cl...

Self-complementary graphs have been extensively investigated and effectively used in the study of Ramsey numbers. It is well-known and easily proved that there exist regular self-complementary graphs of order n if and only if n == 1 (mod 4). So it is natural to ask whether a similar result for self-complementary vertex-transitive graphs exists. More precisely, for which positive integers n do t...

A graph X is called almost self-complementary with respect to a perfect matching I if it is isomorphic to the graph obtained from its complement Xc by removing the edges of I. A two-graph on a vertex set Ω is a collection T of 3-subsets of Ω such that each 4-subset of Ω contains an even number of elements of T . In this paper we investigate the relationship between self-complementary two-graphs...