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arXiv · 2007.12930

Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes

Sadia Noureen·Akhlaq Ahmad Bhatti·Akbar Ali
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Abstract

The Wiener polarity index $W_p$, one of the most studied molecular structure descriptors, was devised by the chemist Harold Wiener for predicting the boiling points of alkanes. The index $W_p$ for chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices at distance 3. A vertex of a chemical tree with the degree at least 3 is called a branching vertex. A segment of a chemical tree $T$ is a path-subtree $S$ whose terminal vertices have degrees different from 2 in $T$ and every internal vertex (if exists) of $S$ has degree 2 in $T$. In this paper, the best possible sharp upper and lower bounds on the Wiener polarity index $W_p$ are derived for the chemical trees of order $n$ with a given number of branching vertices or segments, and the corresponding extremal chemical trees are characterized. As a consequence of the derived results, an open problem concerning the maximal $W_p$ value of chemical trees with a fixed number of segments or branching vertices is solved.

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Sadia Noureen, Akhlaq Ahmad Bhatti, Akbar Ali. 2020-07-25. Towards the Solution of an Extremal Problem Concerning the Wiener Polarity Index of Alkanes. https://doi.org/10.1016/j.chaos.2020.110633

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