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

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.