Bounds for the Kirchhoff Index of Bipartite Graphs

Yujun Yang

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: A (m, n)‐bipartite graph is a bipartite graph such that one bipartition has m vertices and the other bipartition has n vertices. The tree dumbbell D(n, a, b) consists of the path Pn−a−b together with a independent vertices adjacent to one pendent vertex of Pn−a−b and b independent vertices adjacent to the other pendent vertex of Pn−a−b. In this paper, firstly, we show that, among (m, n)‐bipartite graphs (m ≤ n), the complete bipartite graph Km,n has minimal Kirchhoff index and the tree dumbbell D(m + n, ⌊n − (m + 1)/2⌋, ⌈n − (m + 1)/2⌉) has maximal Kirchhoff index. Then, we show that, among all bipartite graphs of order l, the complete bipartite graph K⌊l/2⌋,l−⌊l/2⌋ has minimal Kirchhoff index and the path Pl has maximal Kirchhoff index, respectively. Finally, bonds for the Kirchhoff index of (m, n)‐bipartite graphs and bipartite graphs of order l are obtained by computing the Kirchhoff index of these extremal graphs.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/195242

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:195242

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().