Bounds of Geodetic-Wiener Index on Spirocyclic Graphs (European Journal of Pure and Applied Mathematics, 2025)
Wiener index has been extensively studied for several decades because of its applications in chemistry. Many variants of Wiener index were defined and their corresponding bounds were explored. In this work, we introduced the concept of geodetic-Wiener index by considering the number of geodesics between any pair of vertices. We used the concept of projection of a vertex to a subgraph to decompose the structure into subtrees. Simple spirocyclic graphs are bicyclic graphs whose cycles share a common vertex. Using the idea of partial Wiener index, we determined the bounds of geodetic-Wiener index with respect to other distance-based topological indices for simple spirocyclic graphs.
Keywords: Topological index; Geodetic-Wiener index; Spirocyclic graphs