New concepts of product vague graphs with applications

It is known that vague models give more precision, flexibility and compatibility to the system as compare to the classic and fuzzy models. Vague graph has an important role in neural networks, computer network and clustering. In the design of a network, it is important to analyse connections by the levels. The structural properties of vague graphs provide a tool that identifies a solution to operations research problems. In this paper, we define ring sum of two product vague graph and analyse some interesting properties of isomorphism on product vague graphs.