A Note on Vertex-Edge Wiener Indices of Graphs

Document Type : Research Paper

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Kazerun Branch, Islamic Azad University

Abstract

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|G) and D_2(u,e|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_{ve_1}(G) and W_{ve_2}(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.

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