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 benzenoid hydrocarbons (both cata- and pericondensed) is described, based on the consideration of pairs of elementary cuts of the corresponding benzenoid graph B. A pair of elementary cuts partitions the vertices of B into four classes. WW is expressed as a sum of terms of the form n11n22 + n12n21, each associated with a pair of elementary cuts; nrs, r, s = 1, 2 are the numbers of vertices in the respective four classes. The algorithm proposed enables a relatively easy calculation of WW, finding expressions for WW of homologous series of benzenoid hydrocarbons, and envisaging the relations between WW and molecular structure.