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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/316108 |
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| _version_ | 1832545451867373568 |
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| author | Jianping Ou Xing Feng Saihua Liu |
| author_facet | Jianping Ou Xing Feng Saihua Liu |
| author_sort | Jianping Ou |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8ada87816854409991d0b3292b95f335 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8ada87816854409991d0b3292b95f3352025-02-03T07:25:45ZengWileyJournal 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 |
| spellingShingle | Jianping Ou Xing Feng Saihua Liu On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree Journal of Applied Mathematics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2014/316108 |
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