| Title:
|
The maximum clique and the signless Laplacian eigenvalues (English) |
| Author:
|
Liu, Jianping |
| Author:
|
Liu, BoLian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1233-1240 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Lower and upper bounds are obtained for the clique number $\omega (G)$ and the independence number $\alpha (G)$, in terms of the eigenvalues of the signless Laplacian matrix of a graph $G$. (English) |
| Keyword:
|
bound |
| Keyword:
|
clique number |
| Keyword:
|
independence number |
| Keyword:
|
signless Laplacian eigenvalues |
| MSC:
|
05C50 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1174.05079 |
| idMR:
|
MR2471179 |
| . |
| Date available:
|
2010-07-21T08:16:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140453 |
| . |
| Reference:
|
[1] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs, third ed.Johann Ambrosius Barth Verlag Heidelberg-Leipzig (1995). MR 1324340 |
| Reference:
|
[2] Desai, M., Rao, V.: A characterization of the smallest eigenvalue of a graph.J. Graph Theory 18 (1994), 181-194. Zbl 0792.05096, MR 1258251, 10.1002/jgt.3190180210 |
| Reference:
|
[3] Haemers, W.: Interlacing eigenvalues and graphs.Linear Algebra Appl. 227-228 (1995), 593-616. Zbl 0831.05044, MR 1344588 |
| Reference:
|
[4] Haemers, W., Spence, E.: Enumeration of cospectral graph.Europ. J. Combin. 25 (2004), 199-211. MR 2070541, 10.1016/S0195-6698(03)00100-8 |
| Reference:
|
[5] Lu, M., Liu, H., Tian, F.: Laplacian spectral bounds for clique and independence numbers of graphs.J. Combin. Theory Ser. B 97 (2007), 726-732. Zbl 1122.05072, MR 2344135, 10.1016/j.jctb.2006.12.003 |
| Reference:
|
[6] Motzkin, T., Straus, E. G.: Maxima for graphs and a new proof of a theorem of Turén.Canad. J. Math. 17 (1965), 533-540. MR 0175813, 10.4153/CJM-1965-053-6 |
| . |
