Bounds for the Kirchhoff Index of Bipartite Graphs
A -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent vertices adjacent to the other pendent vertex...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/195242 |
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| _version_ | 1832554204114190336 |
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| author | Yujun Yang |
| author_facet | Yujun Yang |
| author_sort | Yujun Yang |
| collection | DOAJ |
| description | A -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent vertices adjacent to the other pendent vertex of . In this paper, firstly, we show that, among -bipartite graphs , the complete bipartite graph has minimal Kirchhoff index and the tree dumbbell has maximal Kirchhoff index. Then, we show that, among all bipartite graphs of order , the complete bipartite graph has minimal Kirchhoff index and the path has maximal Kirchhoff index, respectively. Finally, bonds for the Kirchhoff index of -bipartite graphs and bipartite graphs of order
are obtained by computing the Kirchhoff index of these extremal graphs. |
| format | Article |
| id | doaj-art-1d3322990b2d44198b68cf984cc0e25c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1d3322990b2d44198b68cf984cc0e25c2025-02-03T05:52:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/195242195242Bounds for the Kirchhoff Index of Bipartite GraphsYujun Yang0School of Mathematics and Information Science, Yantai University, Yantai 264005, ChinaA -bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell consists of the path together with a independent vertices adjacent to one pendent vertex of and b independent vertices adjacent to the other pendent vertex of . In this paper, firstly, we show that, among -bipartite graphs , the complete bipartite graph has minimal Kirchhoff index and the tree dumbbell has maximal Kirchhoff index. Then, we show that, among all bipartite graphs of order , the complete bipartite graph has minimal Kirchhoff index and the path has maximal Kirchhoff index, respectively. Finally, bonds for the Kirchhoff index of -bipartite graphs and bipartite graphs of order are obtained by computing the Kirchhoff index of these extremal graphs.http://dx.doi.org/10.1155/2012/195242 |
| spellingShingle | Yujun Yang Bounds for the Kirchhoff Index of Bipartite Graphs Journal of Applied Mathematics |
| title | Bounds for the Kirchhoff Index of Bipartite Graphs |
| title_full | Bounds for the Kirchhoff Index of Bipartite Graphs |
| title_fullStr | Bounds for the Kirchhoff Index of Bipartite Graphs |
| title_full_unstemmed | Bounds for the Kirchhoff Index of Bipartite Graphs |
| title_short | Bounds for the Kirchhoff Index of Bipartite Graphs |
| title_sort | bounds for the kirchhoff index of bipartite graphs |
| url | http://dx.doi.org/10.1155/2012/195242 |
| work_keys_str_mv | AT yujunyang boundsforthekirchhoffindexofbipartitegraphs |