Graph-Theoretical quantitative structural analysis and modeling of cephalosporin β-Lactam antibiotics through M-Polynomial-Based topological descriptors

• Graph theoretic analysis reveals structural features driving β -lactam class cephalosporins activities • M-polynomials used to derive degree based topological descriptors for cephalosporin drugs • Descriptor-property correlations enable various predictive QSPR modelling analysis • Cubic regression models show strong predictive accuracy across physicochemical properties • Framework supports early-stage screening and rational design of β -lactam antibiotics The increasing prevalence of antimicrobial resistance underscores the need for quantitative approaches to rational drug design, and the understanding of how molecular topology governs physicochemical and biological behavior is also essential. To address this challenge, we developed various quantitative structure property relationship models for the cephalosporin class β -lactam antibiotics utilizing M-polynomial-based topological descriptors. Each cephalosporin molecule is represented as a molecular graph, where the M-polynomial is the degree-based topological framework of these chemical structures, from which the complete set of various topological indices are systematically obtained through operator-based formulations. These descriptors are then statistically correlated to a range of physicochemical properties, such as molecular weight, melting point, molar refractivity, molar volume, polar surface area, polarizability, and toxicity measure also. Statistically significant structure-property relationships with reliable predictive performance, confirming the effectiveness of graph-theoretical descriptors in capturing essential connectivity-driven patterns within the cephalosporin class. The findings of this study establish the M-polynomial method as a unified algebraic tool for molecular characterization, offering a mathematically rigorous and computationally efficient pathway for comparative analysis and early-stage assessment of β -lactam antibiotic structures.