Product vague graphs and its applications.

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we defined the notions of product and complete product vague graphs. We investigated some properties of union, join and complement on product vague graphs and introduced the multiplication of the product vague graphs. Finally we give an application of product vague graphs. Product and complete product vague graphs are highly utilized by computer science, geometry, algebra, number theory and operation research. Likewise, these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones. [ABSTRACT FROM AUTHOR]