An easier enumeration of self-complementary graphs

(-1)-Enumeration of Self-Complementary Plane Partitions

Abstract. We prove a product formula for the remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the sign of the weight. We use nonintersecting lattice path families to express this enumeration as a Pfaffian which can be expressed in terms of the kn...

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...