The topological indices of a graph G are the real numbers associated with its structure, which are important in studying the physicochemical characteristics of the structure of chemical compounds. We provide regression-based analysis of a few medications with different topological indices, examine their correlation coefficient and coefficient of determination \(R^{2}\) , and analyze these physicochemical and topological characteristics. It is noteworthy that there is a stronger correlation between the physical characteristics of these medications and indices, which enhances their effectiveness and progresses their design. In particular, linear, quadratic, and cubic regression models were specifically used to investigate relationships, demonstrating that higher-degree regressions frequently produce better goodness-of-fit values. This study also analyzes linear and quadratic regression models to predict boiling point from topological indices, demonstrating that polynomial models with degree-based indices achieve superior accuracy ( \(R^2 > 0.89\) ). This parallel efficiency makes the models ideal for HPC deployment, enabling rapid virtual screening of anti-HIV compounds at pharmaceutical scales where testing millions of compounds would otherwise be computationally prohibitive.
