On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree

On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree

The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener polarity index of unicyclic graphs with any give...

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Main Authors: Jianping Ou, Xing Feng, Saihua Liu
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/316108
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spelling doaj-8ada87816854409991d0b3292b95f3352020-11-24T23:19:36ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/316108316108On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum DegreeJianping Ou0Xing Feng1Saihua Liu2Department of Mathematics, Wuyi University, Jiangmen 529020, ChinaDepartment of Mathematics, Wuyi University, Jiangmen 529020, ChinaDepartment of Mathematics, Wuyi University, Jiangmen 529020, ChinaThe Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener polarity index of unicyclic graphs with any given maximum degree and girth, and characterize extremal graphs. These observations lead to the determination of the minimum Wiener polarity index of unicyclic graphs and the characterization of the extremal graphs.http://dx.doi.org/10.1155/2014/316108
collection DOAJ
language English
format Article
sources DOAJ
author Jianping Ou
Xing Feng
Saihua Liu
spellingShingle Jianping Ou
Xing Feng
Saihua Liu
On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics
author_facet Jianping Ou
Xing Feng
Saihua Liu
author_sort Jianping Ou
title On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
title_short On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
title_full On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
title_fullStr On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
title_full_unstemmed On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
title_sort on minimum wiener polarity index of unicyclic graphs with prescribed maximum degree
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener polarity index of unicyclic graphs with any given maximum degree and girth, and characterize extremal graphs. These observations lead to the determination of the minimum Wiener polarity index of unicyclic graphs and the characterization of the extremal graphs.
url http://dx.doi.org/10.1155/2014/316108
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AT xingfeng onminimumwienerpolarityindexofunicyclicgraphswithprescribedmaximumdegree
AT saihualiu onminimumwienerpolarityindexofunicyclicgraphswithprescribedmaximumdegree
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