A topological and statistical perspective on carbon nanocones using Kulli-Basava indices

Chemical graph theory stands as a crucial field within mathematical chemistry, boasting diverse applications. Within this discipline, a molecular graph is identified by a numerical measure known as a topological index. Topological indices are one of the main types which can be classified into many categories, with degree-based being most important in chemical graph theory. We investigate the first Kulli-Basava indice (KB Index I) and second Kulli-Basava indices (KB Index II), geometric-arithmetic Kulli-Basava indices (GAKB), hyper Kulli-Basava indices (HKB), as well as certain connectivity Kulli-Basava indices and reciprocal Kulli-Basava indices (RKB) of the Quadrilateral carbon nanocone graph \(\text{CNC}_4[n]\). A comparative statistical analysis reveals that the quadratic regression model demonstrates the highest accuracy in predicting topological properties. Among the examined indices, PKBE (Probably the Best Kulli-Basava Index) exhibits the lowest error values across multiple statistical measures, establishing itself as the most reliable topological descriptor. These findings contribute to the advancement of chemical graph theory by enhancing predictive models for molecular properties and refining structural analysis methodologies, thereby improving the understanding of molecular interactions and material properties.