A New Frontier in Cancer Research: Fuzzy Graph Seidel Signless Laplacian Spectral Analysis for Indian Datasets

This study proposes a new Fuzzy Hamacher Incident Graph framework for modeling complex relational systems in uncertain environments. The developed structure integrates mutually disjoint, symmetric, and irreflexive properties within both edge relations and incidentedge interactions, offering a more flexible and realistic representation of uncertain networks. The method employs a Hamacher-operator-based edge construction strategy to effectively analyze fuzzy graph structures. Furthermore, the proposed method introduces new definitions of graph energy, Laplacian energy, signless Laplacian energy, and Seidel signless Laplacian energy, along with a comparative analysis of their properties, and examines boundary cases to support the theoretical results. Finally, the proposed approach is applied to the cancer impact network of the South Indian region to analyze its structure and identify the optimal alternatives. A dedicated algorithm is also provided to support the practical implementation of the proposed approach in real-world scenarios.