Eccentric connectivity index of some central graphs

Graph theory has become an indispensable branch of contemporary mathematics, contributing significantly to both theoretical and applied research., particularly in the realm of natural sciences such as Chemistry and Biology, due to its various applications. Topological indices are numerical parameters associated with graph isomorphism, which have significance in diverse scientific fields. Research on topological indices has been intensifying in recent times. A topological index denotes a numeric value that encapsulates structural information about a molecule’s graph representation in the chemical graph theory. These indices are based on the topology and bonds of atoms and serve as numerical descriptors. A wide range of topological indices have been developed to capture and evaluate the physicochemical characteristics of molecular structures. Chemical graph theory models molecules as graphs in which atoms are depicted as vertices and chemical bonds as edges. This study concentrates on a particular topological descriptor known as the eccentric connectivity index (ECI), which combines information about vertex degrees and the shortest path distances between them. Here, we investigate and compute the ECI values for certain central graph structures that exhibit distinctive configurations.