An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons

An algorithm for the calculation of the hyper-Wiener index (WW) of benzenoi d hydrocarbons (both cata- and pericondensed) is described, based on the co nsideration of pairs of elementary cuts of the corresponding benzenoid grap h B. A pair of elementary cuts partitions the vertices of B into four class es. WW is expressed as a sum of terms of the form n(11)n(22) + n(12)n(21), each associated with a pair of elementary cuts; n(rs), s = 1, 2 are the num bers of vertices in the respective four classes. The algorithm proposed ena bles a relatively easy calculation of WW, finding expressions for WW of hom ologous series of benzenoid hydrocarbons, and envisaging the relations betw een WW and molecular structure. (C) 2000 Elsevier Science Ltd. All rights r eserved.