Abstract

The vertex-edge Wiener index is a graph invariant defined as the sum of distances between vertices and edges of a graph. In this paper, we study the relation between the first and second vertex-edge Wiener indices of thorn graph and its parent graph and examine several special cases of the results. Results are applied to compute the first and second vertex-edge Wiener indices of thorn stars, Kragujevac trees, and dendrimers.

Keywords: Topological index; thorn graph; bipartite graph; Kragujevac tree; dendrimer.

MSC: 05C12, 05C76

Pages:  263$-$276     

Volume  71 ,  Issue  3 ,  2019