Nessary and sufficient conditions for quasi-strong regularity of graph product

Abstract

A k-regular graph (k ≥ 1) with n vertices is called a quasi-strongly regular graph with parameter λ (λ € N) if any two adjacent vertices have exactly λ neighbors in common. A graph product is a binary operation on graphs. It is useful to describe graph as product of other primitive graphs. In this paper we present some necessary and sufficient conditions for Decartes product. Tensor product, Lexicographical product and Strong product to be quasi-strongly regular.