Indices analysis of hexa organic molecular structures together with fundamental insights of a novel connectivity index

Topological indices play a central role in mathematical chemistry for correlating structural features of molecular graphs with physicochemical properties. Motivated by limitations of existing degree and distance-based descriptors, we introduce a novel connectivity index that counts the d -neighbors (vertices whose distance equals their degree in a connected molecular graph). This new descriptor, called the d -connectivity index, extends classical connectivity frameworks. We establish fundamental theoretical results, including lower bounds, relationships with the first Zagreb index, and expressions for subdivision graphs and graphs of small diameter. Furthermore, we compute and compare the d -connectivity index with six widely used indices for three hexa-organic molecular structures. The findings highlight strong structural sensitivity and the potential applicability of the proposed index in QSPR/QSAR modelling. Moreover, the chemical relevance of the d -connectivity index is established through strong polynomial correlations with multiple physicochemical properties of benzenoid hydrocarbon compounds and octane isomers, confirming its effectiveness as a predictive molecular descriptor.