Some results on the Wiener index of iterated line graphs

The Wiener index W(G) of a graph G is the sum of distances between all unordered pairs of vertices. This notion was motivated by various mathematical properties and chemical applications. For a tree T, it is known that W(T) and W(L(T)) are always distinct. It is shown that there is an infinite family of trees with W(T)=W(L2(T)).