Computation of The Edge Wiener Indices of The Sum of Graphs

Mahdieh Azari1, Ali Iranmanesh2
1Department of Mathematics, Science and Research Branch, Islamic Azad University P. O. Box: 14515-1775, Tehran, Iran
2Department of Mathematics, Tarbiat Modares University P. O. Box: 14115-137, Tehran, Iran

Abstract

The edge versions of Wiener index, which were based on distance between two edges in a connected graph \(G\), were introduced by Iranmanesh et al. in \(2008\). In this paper, we find the edge Wiener indices of the sum of graphs. Then as an application of our results, we find the edge Wiener indices of graphene, \(C_4\)-nanotubes and \(C_4\)-nanotori.