On some Classes of Balanced Graph Designs

Abstract

<p>Necessary and sufficient conditions for the existence of special types of balanced graph designs, namely, balanced bipartite designs, resolved balanced bipartite designs, balanced tripartite designs and balanced circuit designs, are investigated. Given a set of parameters, the necessary conditions for the existence of a design with these parameters are obtained, and to find out whether these conditions are also sufficient, we attempt to construct a collection of base blocks which generate the design. When such a collection cannot be found, we proceed to prove that the particular design does not exist. Several infinite series of designs have also been constructed.</p>