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 ( L 2 ( T ) ) .