Characterization of self-complementary graphs with 2-factors

Characterization of self-complementary graphs with 2-factors

Let G be a self-complementary graph (w.) and ir its degree sbquence. Th ;n G has a 2-factor if and only if R 2 is graphic. This is achieved by ohtaming a structure theorem regarding S.C. graphs without a Z-factor. Another irrreresting corollary of the structure theorem is that if G is a s c. graph of order p 3 N with minimum degree at least p/4, then G has a ?-factor and the result is the best ...

Self-complementary circulant graphs

Self-Complementary Vertex-Transitive Graphs

A graph Γ is self-complementary if its complement is isomorphic to the graph itself. An isomorphism that maps Γ to its complement Γ is called a complementing isomorphism. The majority of this dissertation is intended to present my research results on the study of self-complementary vertex-transitive graphs. I will provide an introductory mini-course for the backgrounds, and then discuss four pr...

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...

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...