Properties of interval valued intuitionistic (S,T) - Fuzzy graphs

The basis of the concept of interval valued intuitionistic fuzzy sets was introduced by K. Atanassov. Interval valued intuitionistic models provide more precision, flexibility, and compatibility to a system than do classic fuzzy models. In this paper, three new types of product operations (direct product, lexicographic product, and strong product) of interval valued intuitionistic (S,T)-fuzzy graphs are defined. One of the most studied classes of fuzzy graphs are regular fuzzy graphs, which appear in many contexts. For example, r-regular fuzzy graphs with connectivity and edge-connectivity equal to r play a key role in designing reliable communication networks. Hence, we introduced the concepts of regular and totally regular interval valued intuitionistic (S,T)-fuzzy graphs. Likewise, we defined busy vertices and free vertices in interval valued intuitionistic (S,T)-fuzzy graphs and studied their images under an isomorphism, which are highly important in fuzzy social networks.