A new construction of regular and quasi-regular self-complementary graphs

A graph $G$ with a vertex set $V$ and an edge set $E$ is called regular if the degree of every vertex is the same. A quasi-regular graph is a graph whose vertices have one of two degrees $r$ and $r-1$, for some positive integer $r$. A graph $G$ is said to be self-complementary if $G$ is isomorphic to it’s complement $\overline{G}$. In this paper we give a new method for construction of regular and quasi-regular self-complementary graph.