Chemical graph theory is a branch of mathematical chemistry that combines chemistry and graph theory. In this field, the topological index is a helpful tool for comprehending physicochemical properties and forecasting the behavior of chemical molecules. The COVID-19 pandemic has underscored the urgent need for effective antiviral therapeutics. Nirmatrelvir, an orally bioavailable SARS-CoV-2 main protease ( \(\hbox {M}^{\text {pro}}\) ) inhibitor co-administered with Ritonavir (Paxlovid), has emerged as a promising treatment. In this study, we present a detailed topological characterization of Nirmatrelvir by deriving several neighborhood degree sum-based topological indices using its NM-polynomial. Furthermore, we present the QSPR analysis using curvilinear regression models among the obtained topological indices and physicochemical properties of the antiviral COVID-19 drugs, such as Molnupiravir, Arbidol, Chloroquine, Hydroxychloroquine, Thalidomide, Remdesivir, Ritonavir, Theaflavin and Lopinavir, including Nirmatrelvir. The results reveal that several considered indices show significant correlations with the physicochemical properties and cubic regression models consistently provide superior predictive accuracy. These findings demonstrate neighborhood degree sum-based topological indices as robust and reliable molecular descriptors in QSPR modelling, highlighting their significant potential for effective prediction of drug properties and their valuable role in facilitating rational drug design and development.
