Computation of The Edge Wiener Indices of The Sum of Graphs

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.