Fuzzy Computational Analysis of Fuzzy Tadpole Graph

Abstract

In this paper, we explore the application of fuzzy topological indices to the fuzzy tadpole graph TA,B, a hybrid structure that combines the cyclic and path-like components within a fuzzy framework. We compute and analyze several key fuzzy indices, including the fuzzy Zagreb indices, fuzzy Randić index, fuzzy Harmonic index, fuzzy Sombor index, fuzzy Misbalance Prodeg index, and fuzzy Nirmala index, to gain a comprehensive understanding of the graph structural and topological properties. Our results reveal how fuzzy indices provide deeper insight into the graph connectivity and stability, especially in scenarios where traditional (crisp) indices may be inadequate. These findings have potential applications in domains such as complex network analysis, molecular chemistry, and systems with inherent uncertainty.