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.
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