The inverse Wiener polarity index problem for chemical trees

PloS One
Zhibin Du, Akbar Ali

Abstract

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

References

Dec 1, 1990·Journal of Biomolecular Structure & Dynamics·V A LapukV P Timofeev
Apr 5, 2003·Journal of Computational Biology : a Journal of Computational Molecular Cell Biology·Xueliang LiLusheng Wang
Dec 23, 2004·Molecular Diversity·Ante MilicevićNenad Trinajstić
Dec 6, 2005·Journal of Computer-aided Molecular Design·Alexandru T Balaban
Jan 1, 1947·Journal of the American Chemical Society·H WIENER
Jan 12, 2016·Scientific Reports·Jing MaJun Yue
Dec 9, 2016·PloS One·Lin ChenHua Wang

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