The edge wiener index of suspensions, bottlenecks, and thorny graphs

Let G be a simple connected graph. The distance between the edges g and f E(G) is defined as the distance between the corresponding vertices g and f in the line graph of G. The edge-Wiener index of G is defined as the sum of such distances between all pairs of edges of the graph. Let G1+G2 and G1ο G2 be the join and the corona of graphs G1 and G2, respectively. In this paper, we present explicit formulas for the edge-Wiener index for these graphs. Then we apply our results to compute the edge-Wiener index of suspensions, bottlenecks, and thorny graphs