Computation of some degree-based topological indices of [n]circulenes according to the size of their central polygon

Abstract

In this paper, several degree-based topological indices are computed for the family of [n]circulenes, a class of polycyclic hydrocarbons, using the M-polynomial method, which eliminates edge counting. Closed-form formulas depending only on the central polygon size n are derived for indices including the First and Second Zagreb, Modified Zagreb, Harmonic, Symmetric Division Degree, Inverse Sum, and Sigma indices. Numerical and graphical analyses for n = 3 to 10 reveal increasing trends, reflecting growing structural complexity. Additionally, an asymptotic analysis explores the behavior of these indices as n → ∞. These results offer a unified and scalable computational framework that fills a theoretical gap and aids quantitative structure–property relationship modeling of complex polycyclic systems.