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RESEARCH ARTICLE

On the edge-Wiener index of the disjunctive product of simple graphs

M. Azari^a, A. Iranmanesh<sup>b

a</sup> Department of Mathematics, Kazerun Branch, Islamic Azad University, P.O. Box: 73135-168, Kazerun, Iran
^b Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box: 14115-137, Tehran, Iran

Abstract: The edge-Wiener index of a simple connected graph $G$ is defined as the sum of distances between all pairs of edges of $G$ where the distance between two edges in $G$ is the distance between the corresponding vertices in the line graph of $G$. In this paper, we study the edge-Wiener index under the disjunctive product of graphs and apply our results to compute the edge-Wiener index for the disjunctive product of paths and cycles.

Keywords: distance in graphs, edge-Wiener index, disjunctive product of graphs.

MSC: 05C76, 05C12, 05C38

Received: 27.06.2016
Revised: 27.09.2017

Language: English

DOI: 10.12958/adm242

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