Topological Index in Shadow Graphs

Mathematical modeling of various natural biological activities has gained significant importance in recent times. In the modeling of these activities, the eccentric connectivity index (ECI) is utilized as a distance-based molecular structure descriptor. This index is defined as epsilon (c)(G) = Sigma v is an element of V(G) deg(v)e(v), where deg(v) and e(v) denote the vertex degree and eccentricity of v, respectively. To support its use as a topological structure descriptor, this study calculates the ECI values of shadow graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.