Abstract
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.
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