Journal of the Serbian Chemical Society 2003 Volume 68, Issue 12, Pages: 949-952
https://doi.org/10.2298/JSC0312949G
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Hyper-Wiener index and Laplacian spectrum
Gutman Ivan 
(Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and Montenegro)
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.
Keywords: hyper-Wiener index, Wiener index, Laplacian spectrum, chemical trees, alkanes