Computational Analysis of Energy, Closeness Energy, and Topological Connectivity in Benzenoid Hydrocarbons

Abstract

Benzenoid hydrocarbons are widely studied molecular structures due to their unique topological and chemical properties. This research investigates
their structural characteristics by evaluating energy, closeness energy, and a range of distance, degree, and eccentricity-based topological indices. The study focuses on the molecular graphs of 22 benzenoid hydrocarbons by aiming to evaluate how energy, closeness energy, and related topological indices can be used to describe structural properties and establish quantitative relationships with physicochemical data. In addition to deriving analytical expressions and performing computational evaluations, we develop regression models to link energy and closeness energy with selected topological indices and intrinsic physicochemical properties. Unlike previous studies that emphasize only tabulated values, our work demonstrates the predictive potential of combining spectral and topological measures, with closeness energy, providing additional insight into the structural characteristics of benzenoid hydrocarbons. The findings provide a clearer understanding of benzenoid structures and contribute to advancing applications of graph-based methods in molecular graph theory, cheminformatics, and materials science.