On some neighborhood degree-based structure descriptors and their applications to graphene

Topological indices are numerical descriptors derived from the structure of molecular graphs, capturing key aspects of their topology and connectivity. They play a vital role in cheminformatics by correlating molecular structure with physical, chemical, and biological properties, enabling efficient property predictions and molecular design. In this article, we explored the applicability of several neighborhood degree-based structural descriptors, including the fifth M-Zagreb indices, fifth hyper-M-Zagreb indices, and NDe indices, in predicting key thermodynamic properties of benzenoid hydrocarbons. These indices serve as mathematical tools to capture structural and topological features of molecular graphs, providing valuable insights into molecular behavior. Our analysis demonstrates that these indices exhibit strong correlations with critical thermodynamic properties such as boiling point, entropy, enthalpy of formation, Kovats retention index, and octanol-water partition coefficient of benzenoid hydrocarbons. Among the studied descriptors, the fourth NDe index showed particularly impressive performance, with correlation coefficients exceeding 0.97 for all considered properties. These findings highlight the potential of neighborhood degree-based indices as reliable predictors of molecular properties, offering a cost-effective and computationally efficient alternative to experimental methods. Furthermore, the results underscore the utility of graph-theoretic descriptors in the broader context of cheminformatics and property prediction for organic compounds, paving the way for future research into their applications across diverse molecular systems.