Optimizing wireless sensor networks using fuzzy triangular snake graph models and fuzzy topological indices

This research focuses on a detailed investigation of advanced fuzzy indices applied to enhanced version of triangular snake graph, designated as fuzzy triangular snake graph (). Its practical applications in wireless sensor network (WSN) is also designed. We derive closed-form formulas for several fuzzy indices, including first and second fuzzy Zagreb indices, fuzzy Harmonic, Randić, Misbalance Prodeg, Nirmala, along with Sombor indices. By applying these indices to a WSN modeled with redundant triangular connectivity, we evaluate the network’s structural efficiency, robustness, and fault tolerance. The computed results reveal that the fuzzy triangular snake topology ensures balanced node connectivity, minimizes energy imbalance, and enhances the network’s ability to maintain reliable communication in the presence of node failures and uncertainties. The results confirm the applicability of the fuzzy triangular snake model in optimization of energy- and resilient WSNs, thus drawing a high degree of correlation between such contemporary graph theory, as fuzziness, and the design of a modern communication network.