A Novel NM-Polynomial Approach to QSPR Analysis of Anti-Diabetic Drugs Using Neighborhood Degree-Based Topological indices

Diabetes mellitus, a complex metabolic disorder, necessitates the continuous development of effective therapeutics. In this article, we employ a Quantitative Structure-Property Relationship (QSPR) paradigm to analyze ten prominent antidiabetic drugs. Using chemical graph theory, the molecular graphs of these drugs were constructed, and an advanced computational framework based on the NM-polynomial was utilized to simultaneously derive thirteen neighborhood degree sum-based topological indices (TI). These indices, including the Neighborhood Zagreb indices, Neighborhood Harmonic index, and Neighborhood Inverse Sum index, served as numerical descriptors to model eight crucial physicochemical properties: Boiling Point (BP), Enthalpy of Vaporization (EV), Flash Point (FP), Molar Refractivity (MR), Polar Surface Area (PSA), Polarizability (PO), Molar Volume (MV), and Refractive Index (IR). Linear regression models revealed strong and statistically significant correlations (p < 0.05) between these topological indices and the drug properties. Specifically, the Neighborhood Modified Second Zagreb index (NmM₂) showed the highest correlation with BP and MV (r = 0.920 and r = 0.945, respectively), while the Neighborhood Sum Connectivity index (NSCI) was a superior predictor for MR and PO (r = 0.969 for both). These results validate the predictive power of the NM-polynomial approach and underscore its efficacy as a reliable computational tool for the design and optimization of antidiabetic drugs with desirable physicochemical profiles. The findings of this article can pave the way for developing the next generation of diabetes therapeutics.