Correlation Ability of Degree-Based Topological Indices for Physicochemical Properties of Polycyclic Aromatic Hydrocarbons with Applications

Several chemical and medical experimentation reveals a dependence of physicochemical and biological properties of a compound on its molecular structure. Molecular/topological descriptors/indices retrieve this dependence by employing mathematical/statistical tools to generate quantitative structure property/activity relationship (QSAR/QSPR) models. QSAR/QSPR models are regression models which theoretically relate a physicochemical/biological property to a molecular descriptor. By converting a compound to a chemical graph, graph-theoretic topological indices use algorithmic graph theory to generate QSAR/QSPR models. Degree-related molecular indices have been well-known for correlating better with certain physicochemical characteristics of compounds. In this paper, we conduct a comparative analysis to put forward the best degree-based index for correlating with physicochemical characteristics of polycyclic aromatic hydrocarbons. Two different computational techniques have been put forward and then used to conduct our comparative analysis. Our comparative testing generates several favorable and unexpected conclusions as the well-known indices such as the augmented Zagreb index, the atom-bond connectivity index, the geometric arithmetic index deliver relatively poor performance. Moreover, exceptional performance of the generalized variants of Randic and sum-connectivity indices is somehow unexpected as they significantly outperform the well-studied and well-researched degree-based indices. This warrants to study further the general Randic and sum-connectivity indices for QSAR/QSPR models. Applications to certain families of carbon polyhex aromatic nanotubes are reported.