Comparative Study of rth Chain Benzenoid Hex-Derived Network

This study integrates advanced algorithms with chemical graph theory to analyze the topological indices of benzenoid-derived nanostructures, focusing on their applications in computational chemistry and drug design. By developing novel mathematical formulations for degree-based indices (Rα, M1, H, AZI, ABC, and GA), we establish quantitative relationships between structural parameters (r, s) and physicochemical properties of hexagonal networks. Our results reveal that increasing network dimensions enhances molecular stability and electron delocalization in these nanostructures, offering critical insights for optimizing antiviral agents and energy storage materials. The proposed computational framework, validated through rigorous graphical and tabular comparisons, provides a robust tool for predicting structure-activity relationships in drug discovery and designing next-generation nanomaterials. This work bridges theoretical graph theory with practical applications in nanotechnology and pharmaceutical sciences, demonstrating significant potential for sustainable innovation in medical and energy technologies.