Bounds for the Kirchhoff Index of Bipartite Graphs

Yujun Yang

Journal of Applied Mathematics, 2012, vol. 2012, 1-9

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:195242

DOI: 10.1155/2012/195242

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