Some new results on domination in fuzzy graphs

Abstract

Generally, it is a difficult task to determine the exact domination or total domination number of a product graph. Thus obtaining upper or lower bounds of the same remains an interesting research topic in the theory of fuzzy logic and soft computing. In this paper we study the theory of domination in the context of product fuzzy graph. We define the concepts of domination and total domination in the setting of direct product of two fuzzy graphs. Further, we obtain an upper bound for the total domination number of the product fuzzy graph.