Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 195242, 9 pages.
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 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.
J. Appl. Math., Volume 2012 (2012), Article ID 195242, 9 pages.
First available in Project Euclid: 14 December 2012
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Yang, Yujun. Bounds for the Kirchhoff Index of Bipartite Graphs. J. Appl. Math. 2012 (2012), Article ID 195242, 9 pages. doi:10.1155/2012/195242. https://projecteuclid.org/euclid.jam/1355495113