A Note on Vertex-Edge Wiener Indices of Graphs

The vertex-edge Wiener index of a simple connected graph G is defined as the sum of distances between vertices and edges of G. Two possible distances D-1(u, e vertical bar G) and D-2(u, e vertical bar G) between a vertex u and an edge e of G were considered in the literature and according to them, the corresponding vertex-edge Wiener indices W-ve1 (G) and W-ve2 (G) were introduced. In this paper, we present exact formulas for computing the vertex-edge Wiener indices of two composite graphs named splice and link.