Mathematical and Chemical Analysis of Wiener's Polarity Number

Hosoya, Haruo; Gao, Ying-Duo

doi:10.1016/b978-1-898563-76-1.50007-x

Cited by 17 publications

(15 citation statements)

References 23 publications

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“…In 1998, by using the Wiener polarity index, Lukovits and Linert [ 2 ] demonstrated quantitative structure-property relationships in a series of acyclic and cycle-containing hydrocarbons. Besides, a physical-chemical interpretation of W p ( G ) was found by Hosoya [ 3 ]. Recently, Du et al [ 4 ] obtained the smallest and largest Wiener polarity indices together with the corresponding graphs among all trees on n vertices, respectively.…”

Section: Introductionmentioning

confidence: 96%

On the Extremal Wiener Polarity Index of Hückel Graphs

Wang

2016

Computational and Mathematical Methods in Medicine

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Graphs are used to model chemical compounds and drugs. In the graphs, each vertex represents an atom of molecule and edges between the corresponding vertices are used to represent covalent bounds between atoms. The Wiener polarity index W p(G) of a graph G is the number of unordered pairs of vertices u, v of G such that the distance between u and v is equal to 3. The trees and unicyclic graphs with perfect matching, of which all vertices have degrees not greater than three, are referred to as the Hückel trees and unicyclic Hückel graphs, respectively. In this paper, we first consider the smallest and the largest Wiener polarity index among all Hückel trees on 2n vertices and characterize the corresponding extremal graphs. Then we obtain an upper and lower bound for the Wiener polarity index of unicyclic Hückel graphs on 2n vertices.

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Section: Introductionmentioning

confidence: 96%

On the Extremal Wiener Polarity Index of Hückel Graphs

Wang

2016

Computational and Mathematical Methods in Medicine

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“…By using the Wiener polarity index, the authors in [4] demonstrated quantitative structure-property relationships in a series of acyclic and cycle-containing hydrocarbons. Hosoya [5] found a physical-chemical interpretation of W P (G). Recently, the trees (resp.…”

Section: Introductionmentioning

confidence: 98%

On the Wiener polarity index of trees with maximum degree or given number of leaves

Liu¹,

Hou²,

Huang³

2010

Computers & Mathematics with Applications

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a b s t r a c tThe Wiener polarity index W P (G) of a graph G = (V , E) is the number of unordered pairs of vertices {u, v} of G such that the distance d G (u, v) = 3. In this paper, the minimum (resp. maximum) Wiener polarity index of trees with n vertices and maximum degree ∆ are given, and the corresponding extremal trees are determined, where 2 ≤ ∆ ≤ n − 1. Moreover, the trees minimizing W P (T ) among all trees T of order n and k leaves are characterized, where 2 ≤ k ≤ n − 1.

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“…In 1998, Lukovits and Linert [5] demonstrated quantitative structure-property relationships in a series of acyclic and cyclecontaining hydrocarbons by using the Wiener polarity index. In 2002, Hosoya [6] found a physicochemical interpretation of W P (G). Du et al [7] obtained the smallest and largest Wiener polarity indices together with the corresponding graphs among all trees on n vertices, respectively.…”

Section: Introductionmentioning

confidence: 99%