Klavžar, Sandi; Žigert, Petra; Gutman, Ivan An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons. (English) Zbl 1034.92040 Comput. Chem. 24, No. 2, 229-233 (2000). 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. Cited in 16 Documents MSC: 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.) 05C90 Applications of graph theory Keywords:hyper-Wiener index; Benzenoid hydrocarbons; topological index; Benzenoid graph; elementary cut PDFBibTeX XMLCite \textit{S. Klavžar} et al., Comput. Chem. 24, No. 2, 229--233 (2000; Zbl 1034.92040) Full Text: DOI Online Encyclopedia of Integer Sequences: The hyper-Wiener index of the circumcoronene H(n) (see definition in the Klavzar papers). Triangle read by rows: T(n,k) is the number of unordered pairs of nodes at distance k in the circumcoronene H(n) (n=1,2,3,4,5; see definition in the Klavzar papers).