A Note on the Minimum Wiener Polarity Index of Trees with a Given Number of Vertices and Segments or Branching Vertices

Sadia Noureen, Akhlaq Ahmad Bhatti, Akbar Ali and Juan L. G. Guirao

Discrete Dynamics in Nature and Society, 2021, vol. 2021, 1-5

Abstract: The Wiener polarity index of a graph G, usually denoted by WpG, is defined as the number of unordered pairs of those vertices of G that are at distance 3. A vertex of a tree with degree at least 3 is called a branching vertex. A segment of a tree T is a nontrivial path S whose end-vertices have degrees different from 2 in T and every other vertex (if exists) of S has degree 2 in T. In this note, the best possible sharp lower bounds on the Wiener polarity index Wp are derived for the trees of fixed order and with a given number of branching vertices or segments, and all the trees attaining this lower bound are characterized.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:1052927

DOI: 10.1155/2021/1052927

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