On the Extremal Wiener Polarity Index of Hückel Graphs

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 vert...

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Bibliographic Details
Published in:Computational and mathematical methods in medicine 2016-01, Vol.2016 (2016), p.1-6
Main Author: Wang, Hongzhuan
Format: Article
Language:English
Subjects:
Algorithms
Chemistry, Organic - methods
Chemistry, Pharmaceutical - methods
Drug Design
Models, Statistical
Statistics as Topic
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Summary: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 2 n 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 2 n vertices.
ISSN:1748-670X
1748-6718
DOI:10.1155/2016/3873597