| Title:
|
On the multiplicity of Laplacian eigenvalues of graphs (English) |
| Author:
|
Guo, Ji-Ming |
| Author:
|
Feng, Lin |
| Author:
|
Zhang, Jiong-Ming |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
689-698 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the effect on the multiplicity of Laplacian eigenvalues of two disjoint connected graphs when adding an edge between them. As an application of the result, the multiplicity of 1 as a Laplacian eigenvalue of trees is also considered. (English) |
| Keyword:
|
Laplacian eigenvalue |
| Keyword:
|
multiplicity |
| Keyword:
|
tree |
| Keyword:
|
characteristic polynomial |
| MSC:
|
05C50 |
| idZBL:
|
Zbl 1224.05297 |
| idMR:
|
MR2672410 |
| . |
| Date available:
|
2010-07-20T17:10:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140599 |
| . |
| Reference:
|
[1] Cvetković, D. M., Doob, M., Sachs, H.: Spectra of Graphs-Theory and Application.Deutscher Verlag der Wissenschaften - Academic Press, Berlin-New York, 1980; second edition 1982; third edition, Johann Ambrosius Barth Verlag, Heidelberg-Leipzig (1995). |
| Reference:
|
[2] Faria, I.: Permanental roots and the star degree of a graph.Linear Algebra Appl. 64 (1985), 255-265. Zbl 0559.05041, MR 0776531, 10.1016/0024-3795(85)90281-2 |
| Reference:
|
[3] Grone, R., Merris, R., Sunder, V. S.: The Laplacian spectrum of a graph.SIAM J. Matrix Anal. Appl. 11 (1990), 218-238. Zbl 0733.05060, MR 1041245, 10.1137/0611016 |
| Reference:
|
[4] Grone, R., Merris, R.: The Laplacian spectrum of a graph II*.SIAM J. Discrete Math. 7 (1994), 221-229. Zbl 0795.05092, MR 1271994, 10.1137/S0895480191222653 |
| Reference:
|
[5] Guo, J. M.: On the second largest Laplacian eigenvalue of trees.Linear Alg. Appl. 404 (2005), 251-261. Zbl 1066.05085, MR 2149662, 10.1016/j.laa.2005.02.031 |
| Reference:
|
[6] Mohar, B.: The Laplacian spectrum of graphs.Graph Theory, Combinatorics, and Applications 2 (1991), 871-898. Zbl 0840.05059, MR 1170831 |
| Reference:
|
[7] Shao, J. Y., Guo, J. M., Shan, H. Y.: The ordering of trees and connected graphs by algebraic connectivity.Linear Alg. Appl. 428 (2008), 1421-1438. Zbl 1134.05063, MR 2388629 |
| . |
