Hyper-Wiener index and Laplacian spectrum

摘要

The hyper-Wiener index WWW of a chemical tree T is defined as the sum of the product n_1 n_2 n_3, over all pairs u, v of vertices of T, where n_1 and n_2 are the number of vertices of T, lying on the two sides of the path which connects u and v, and n_3 is the number of vertices lying between u and v. An expression enabling the calculation of WWW from the Laplacian eigenvalues of T has been deduced.