Numerical Prediction of Physicochemical Properties of Drug Structures via Some Graph Parameters

Graph theory has become a fundamental mathematical framework with broad applications across various scientific fields, such as biology, network security, computer science, and chemistry. A specialized branch known as chemical graph theory employs graph-based mathematical principles to model and analyze molecular architectures. Typically, molecular graphs are generated from 2D representations of chemical structures, where physicochemical properties play a decisive role in interpreting a molecule’s physical and chemical behavior. Structural symmetry within these molecular graphs significantly aids in deriving fundamental graph parameters. Recently, a novel theoretical method has been introduced to perform a comparative analysis of seven significant domination parameters alongside the p-electronic energy of benzenoid hydrocarbons. In the field of graph theory, the independence, covering, and domination numbers stand as fundamental parameters. Inspired by this methodology and related research, this study presents an exploratory investigation into the physicochemical properties of 10 selected drug and bioactive molecules from diverse therapeutic classes to evaluate bulk size-dependent properties using these fundamental graph parameters. Various regression models were evaluated alongside leave one out cross validation (LOOCV) diagnostics for six specific properties of these compounds: boiling point (BP), enthalpy of vaporization (EV), flash point (FP), molar refractivity (MR), polarizability (P), and molar volume (MV). The results highlight the potential of these fundamental graph parameters in QSPR modeling, establishing an exploratory proof of concept that warrants future support from more comprehensive independent datasets.