On diameter and girth of product of zero-divisor graphs

Abstract

Graph theory has become a hot topic in Mathematics due to the gradual research done in graph theory. Product of graphs enables the combination or decomposition of its elemental structures. In graph theory there are four standard products, each with its own set of applications and theoretical interpretations. In this article, we study these graph products of zero-divisor graphs of commutative rings and determine their structural properties such as connectivity, diameter and girth. We also determine when the graph product of zero-divisor graphs of ring Zn and Zm are Eulerian.