In this paper, -product of two fuzzy graphs is introduced and proved that the -product of two regular fuzzy graphs need not be regular and also if  is regular, then  (or)  need not be regular. A necessary and sufficient condition for  to be a regular fuzzy graph is determined. The degree of vertices in  in terms of those in  and  is determined for some particular cases and regular properties of  are studied.

regular fuzzy graph, product of fuzzy graph, complete graph, regular graph, complement graph.