Relation between hyper-Wiener and Wiener index

An identity between the hyper-Wiener index (WW) and the Wiener index (W) of a tree is deduced, showing that these two molecular-structure-descriptors are more intimately connected than earlier believed. Let T be a tree on n vertices and e be its edge. Let T1(e) and T2(e) be the components of the disconnected graph obtained by deleting e from T. Then WW(T)=(n/2)W(T)−(1/2)∑e[W(T1(e))+W(T2(e))] with the summation embracing all edges of T.