Insights into IF-Geodetic Convexity in Intuitionistic Fuzzy Graphs: Harnessing the IF-Geodetic Wiener Index for Global Human Trading Analysis and IF-Geodetic Cover for Gateway Node Identification

To offer a viewpoint on convexity and connectedness inside intuitionistic fuzzy graphs (IFGs), the paper is devoted to the study of intuitionistic fuzzy geodetic convexity. The paper introduces an algorithm for precise identification and characterization of geodetic pathways in IFGs, supported by a Python program. Various properties of IF-geodetic convex sets such as IF-internal and IF-boundary vertices are obtained. Furthermore, this work introduces and characterizes the concepts of geodetic IF-cover, geodetic IF-basis, and geodetic IF-number. Additionally, the study develops the IF-geodetic Wiener index. The scope of the work explores the application of IF-geodetic cover in wireless mesh networks, focusing on the identification of gateway nodes, where symmetry in connectivity patterns enhances network efficiency. A practical implementation of the IF-geodetic Wiener index method in global human trading analysis underscores the real-world implications of the developed concepts, where the efficiency and interpretability of fuzzy geodetic measures are improved by symmetry in network topologies and trade patterns.