Analysis of M-polynomial and NM – polynomial Graphs in Topographies using Fuzzy Mathematical Modeling

Abstract

Objective: Molecular topology, chemical-based graph theory, and mathematical chemistry all depend on the study of topological criteria because these metrics capture the structural, chemical, and physical properties of molecules. However, there is a clear challenge in characterising non-isomorphic graphs that have the same topological measure value. Numerous areas of chemistry benefit from the application of algebraic graph theory. It is a strong theoretical method for predicting either the common and unusual properties of molecules because it clarifies how the many orientations of macromolecules and crystals impact their structure and behaviour.
Methods : In this study, we first calculate the M and NM polynomials of the graph and then recover some degree-based and neighbourhood degree sum based indices. In addition, a few outcomes are shown graphically for contrast.
Findings : First Zagreb Index (U_1), Second Zagreb Index (U_2), Redefined third Zagreb Index (U_3), Y-Tally (U_y), Forgotten topological Index (U_f ), Second modified Zagreb Index (U_m), Symmetric division deg Index (U_d ), Harmonic Index (U_h), Inverse sum indeg Index (U_i), and Augmented Zagreb Index (U_a) are among the topographies of the Graph that this work aims to forecast and analyse using fuzzy mathematical modelling.
Novelty: This research used ANOVA one-way classification to show that the graph's various topographies are the same.