Self-complementary two-graphs and almost self-complementary double covers

Two-graphs, Double Covers over Complete Graphs, and Almost Self-complementary Graphs

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...

On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements Xc − I, where Xc denotes the complement of X and I a perfect matching (1-factor) in Xc. Almost self-complementary circulant graphs were first studied by Dobson and Šajna in 2004. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In par...

Homogeneously almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to the graph obtained from its complement by removing a 1-factor. In this paper, we study a special class of vertex-transitive almost self-complementary graphs called homogeneously almost selfcomplementary. These graphs occur as factors of symmetric index-2 homogeneous factorizations of the “cocktail party graphs” K2n − nK2. We con...

Brick assignments and homogeneously almost self-complementary graphs

Article history: Received 9 February 2005 Available online 7 July 2008

Self-complementary circulant graphs