Comparative Analysis of Cardinality and Isomorphism in Intuitionistic and Neutrosophic Fuzzy Graph Theory

This paper explores the cardinality and isomorphic properties of intuitionistic fuzzy graph theory (IFGT) and neutrosophic fuzzy graph theory (NFGT). Graph theory has evolved significantly with the introduction of fuzzy concepts, enhancing the modeling of uncertainty and vagueness. Intuitionistic fuzzy graphs (IFGs) extend traditional fuzzy graphs by incorporating both membership and non-membership degrees, while neutrosophic fuzzy graphs (NFGs) introduce a three-dimensional approach with truth, indeterminacy, and falsity degrees. We analyze the cardinality and isomorphic properties of these graph structures, highlighting their mathematical foundations, comparative aspects, and potential applications