Hyper-Wiener index and Laplacian spectrum

The hyper-Wiener index WWW of a chemical tree T is defined as the sum of the product n1 n2 n3, over all pairs υ,ν of vertices of T, where n1 and n2 are the number of vertices of T, lying on the two sides of the path which connects υ and ν, and n3 is the number of vertices lying between υ and ν. An expression enabling the calculation of WWW from the Laplacian eigenvalues of T has been deduced.