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An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons. (English) Zbl 1034.92040

Summary: 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 \(n_{11}n_{22}+ n_{12}n_{21}\), each associated with a pair of elementary cuts; \(n_{rs},r\), \(s=1,2\), 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.

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
05C90 Applications of graph theory
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