The maximum clique and the signless Laplacian eigenvalues
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1233-1240 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $G$.
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 $G$.
Classification : 05C50, 05C69
Keywords: bound; clique number; independence number; signless Laplacian eigenvalues
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Liu, Jianping; Liu, BoLian. The maximum clique and the signless Laplacian eigenvalues. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1233-1240. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a26/

[1] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs, third ed. Johann Ambrosius Barth Verlag Heidelberg-Leipzig (1995). | MR

[2] Desai, M., Rao, V.: A characterization of the smallest eigenvalue of a graph. J. Graph Theory 18 (1994), 181-194. | DOI | MR | Zbl

[3] Haemers, W.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 227-228 (1995), 593-616. | MR | Zbl

[4] Haemers, W., Spence, E.: Enumeration of cospectral graph. Europ. J. Combin. 25 (2004), 199-211. | DOI | MR

[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. | DOI | MR | Zbl

[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. | DOI | MR