M polynomial and degree based topological indices of six common synthetic polymers

The M-polynomial is a powerful algebraic tool that encodes structural information of molecular graphs and enables the derivation of numerous degree-based topological indices through algebraic operations. In this paper, we compute the general forms of M-polynomials for six widely used synthetic polymers modeled as linear chains of n repeating monomer units: Polyethylene (PE), Polypropylene (PP), Polyvinyl Chloride (PVC), Polystyrene (PS), Nylon-6,6, and Polyethylene Terephthalate (PET). Using hydrogen-suppressed molecular graphs, we derive the edge partitions based on vertex degrees for each polymer chain and express the M-polynomials as explicit functions of the chain length parameter n. From these M-polynomials, eleven degree-based topological indices are computed, including the first and second Zagreb indices, the modified second Zagreb index, the general Randić index, the symmetric division degree index, the harmonic index, the inverse sum index, the augmented Zagreb index, the atom-bond connectivity index, and the geometric-arithmetic index. Three-dimensional surface plots of the M-polynomials and comparative analyses of the topological indices across all six polymers are presented. The results reveal distinctive structural characteristics of each polymer class and demonstrate the utility of M-polynomials in the systematic study of polymer molecular topology. Furthermore, we discuss the relevance of these computations to quantitative structure-property relationship (QSPR) studies for predicting physicochemical properties of polymers.