Trees with extremal hyper-Wiener index: Mathematical basis and chemical applications

Ivan Gutman, Wolfgang Linert, István Lukovits, Andrey A. Dobrynin

Research output: Contribution to journalArticle

53 Citations (Scopus)


Trees with minimal and maximal hyper-Wiener indices (WW) are determined: Among n-vertex trees, minimum and maximum WW is achieved for the star-graph (Sn) and the path-graph (Pn), respectively. Since WW(Sn) is a quadratic polynomial in n, whereas WW(Pn) is a quartic polynomial in n, the hyper-Wiener indices of all n-vertex trees assume values from a relatively narrow interval. Consequently, the hyper-Wiener index must have a very low isomer-discriminating power. This conclusion is corroborated by finding large families of trees, all members of which have equal WW-values.

Original languageEnglish
Pages (from-to)349-354
Number of pages6
JournalJournal of Chemical Information and Computer Sciences
Issue number2
Publication statusPublished - Jan 1 1997

ASJC Scopus subject areas

  • Chemistry(all)
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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