β-PRODUCT OF VAGUE GRAPH

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 introduce the notions of β-product of two vague graphs and we proved that the β-product of two regular vague graphs need not be regular and that if G_1 x_β^v G_2is regular, then G_1 or G_2 need not be regular. A necessery and sufficient condition for G_1 x_β^v G_2 to be a regular vague graph is determined. The degree of vertices in G_1 x_β^v G_2in terms of these in G_1 and G_2are determined for some particular cases and regular property of G_1 x_β^v G_2 is studied.