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

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.