Hyper-Wiener index and Laplacian spectrum

Ivan Gutman
2003 Journal of the Serbian Chemical Society  
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, u 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 u, and n 3 is the number of vertices lying between u and u. An expression enabling the calculation of WWW from the Laplacian eigenvalues of T has been deduced.
doi:10.2298/jsc0312949g fatcat:dwqtwjy2qza67awuolctnt5p6m