Topological characterization of [n]-triangulenes through degree-based molecular descriptors with the prediction to π-electron energy

Abstract Triangulene and its π -extended homologues are a family of polycyclic aromatic hydrocarbons with a peculiar chemical structure. They are recognized for their intricate structural configurations and electrical properties, which make them a promising material for potential uses in spintronics. They are built of benzenoid rings fused in a triangular manner. Topological indices are widely utilized as graph theoretical measures for evaluating the physicochemical properties of polycyclic aromatic hydrocarbons by analyzing their molecular structures, makes them hold a significant position in the domain of mathematical and computational chemistry. In this study, a mathematical exploration of topological indices of [ n ]-triangulenes has been done to establish a comprehensive understanding of their applications and significance. Generalized expressions for topological indices have been computed, and their predictive power for various physicochemical properties has been studied using statistical methods. Also, a quantitative structure-property relationship analysis of [ n ]-triangulene's energetic characteristics has been performed. Moreover, a generalized algebraic expression to predict the π -electron energy of [ n ]-triangulene structure has been derived.