The maximum clique and the signless Laplacian eigenvalues

Jianping Liu; Bo Lian Liu

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1233-1240
  • ISSN: 0011-4642

Abstract

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Lower and upper bounds are obtained for the clique number ω ( G ) and the independence number α ( G ) , in terms of the eigenvalues of the signless Laplacian matrix of a graph G .

How to cite

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Liu, Jianping, and Liu, Bo Lian. "The maximum clique and the signless Laplacian eigenvalues." Czechoslovak Mathematical Journal 58.4 (2008): 1233-1240. <http://eudml.org/doc/37899>.

@article{Liu2008,
abstract = {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 $G$.},
author = {Liu, Jianping, Liu, Bo Lian},
journal = {Czechoslovak Mathematical Journal},
keywords = {bound; clique number; independence number; signless Laplacian eigenvalues; bound; clique number; independence number; signless Laplacian eigenvalues},
language = {eng},
number = {4},
pages = {1233-1240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The maximum clique and the signless Laplacian eigenvalues},
url = {http://eudml.org/doc/37899},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Liu, Jianping
AU - Liu, Bo Lian
TI - The maximum clique and the signless Laplacian eigenvalues
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1233
EP - 1240
AB - 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 $G$.
LA - eng
KW - bound; clique number; independence number; signless Laplacian eigenvalues; bound; clique number; independence number; signless Laplacian eigenvalues
UR - http://eudml.org/doc/37899
ER -

References

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  1. Cvetković, D., Doob, M., Sachs, H., Spectra of Graphs, third ed, Johann Ambrosius Barth Verlag Heidelberg-Leipzig (1995). (1995) MR1324340
  2. Desai, M., Rao, V., 10.1002/jgt.3190180210, J. Graph Theory 18 (1994), 181-194. (1994) Zbl0792.05096MR1258251DOI10.1002/jgt.3190180210
  3. Haemers, W., Interlacing eigenvalues and graphs, Linear Algebra Appl. 227-228 (1995), 593-616. (1995) Zbl0831.05044MR1344588
  4. Haemers, W., Spence, E., 10.1016/S0195-6698(03)00100-8, Europ. J. Combin. 25 (2004), 199-211. (2004) MR2070541DOI10.1016/S0195-6698(03)00100-8
  5. Lu, M., Liu, H., Tian, F., 10.1016/j.jctb.2006.12.003, J. Combin. Theory Ser. B 97 (2007), 726-732. (2007) Zbl1122.05072MR2344135DOI10.1016/j.jctb.2006.12.003
  6. Motzkin, T., Straus, E. G., 10.4153/CJM-1965-053-6, Canad. J. Math. 17 (1965), 533-540. (1965) MR0175813DOI10.4153/CJM-1965-053-6

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