Bounds for the Kirchhoff Index of Bipartite Graphs
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-04-23
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Yang, Yujun. 2012. Bounds for the Kirchhoff Index of Bipartite Graphs. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993027
Modern Language Association (MLA)
Yang, Yujun. Bounds for the Kirchhoff Index of Bipartite Graphs. Journal of Applied Mathematics No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-993027
American Medical Association (AMA)
Yang, Yujun. Bounds for the Kirchhoff Index of Bipartite Graphs. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993027
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993027