Enumeration of unlabelled graphs with specified degree parities

AbstractThis paper gives a generating function for unlabelled graphs of order n. The coefficient of each monomial in this function shows the number of unlabelled graphs with given size and the number of odd vertices. Furthermore, the numerical examples are given for 1⩽n⩽9

On separable self-complementary graphs

AbstractIn this paper, we describe the structure of separable self-complementary graphs

A series of search designs for 2 m factorial designs of resolution V which permit search of one or two unknown extra three-factor interactions

Search design, minimum treatment, balanced array, strength 6, weighted graph, isomorphic graph,