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Keywords:
bound; clique number; independence number; signless Laplacian eigenvalues
bound; clique number; independence number; signless Laplacian eigenvalues
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 $G$.
References:
[1] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs, third ed. Johann Ambrosius Barth Verlag Heidelberg-Leipzig (1995). MR 1324340
[2] Desai, M., Rao, V.: A characterization of the smallest eigenvalue of a graph. J. Graph Theory 18 (1994), 181-194. DOI 10.1002/jgt.3190180210 | MR 1258251 | Zbl 0792.05096
[3] Haemers, W.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 227-228 (1995), 593-616. MR 1344588 | Zbl 0831.05044
[4] Haemers, W., Spence, E.: Enumeration of cospectral graph. Europ. J. Combin. 25 (2004), 199-211. DOI 10.1016/S0195-6698(03)00100-8 | MR 2070541
[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 10.1016/j.jctb.2006.12.003 | MR 2344135 | Zbl 1122.05072
[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 10.4153/CJM-1965-053-6 | MR 0175813
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