Quantitative Analysis of Status-Based Topological Indices for Predictive Modeling of Molecular Properties

Abstract

Polycyclic aromatic hydrocarbons (PAHs) are a class of aromatic molecules consisting of multiple fused benzene rings. In chemical graph theory, topological indices play a crucial role in exploring structure-property relationships and in forecasting physicochemical behavior and biological responses of PAH compounds. Such indices are extensively utilized in computational chemistry, drug discovery, and quantitative structure-property relationship (QSPR) modeling. In this work, we investigate the predictive capability of several status-based topological indices, namely the First Status Connectivity index S_1 (G), Second Status Connectivity index S_2 (G), Nirmala Status index SN(G), Forgotten Status index SF(G), Status Sombor index SSO(G), and Status Elliptic Sombor index SESO(G) for a selected set of 38 high-priority PAHs. Among the studied descriptors, the Nirmala Status index exhibits the highest predictive accuracy, particularly for molar refractivity and polarizability (R ≈ 0.979). Furthermore, the variation in the best-performing index across linear, quadratic, and cubic regression models is illustrated in comparative plots based on minimum RMSE values, providing greater clarity and interpretation. The results demonstrate that status-based indices effectively capture long-range structural and electronic characteristics of PAHs. This study highlights the potential of distance-based topological descriptors as reliable tools in QSPR modeling.