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Laplacian spectral bounds for clique and independence numbers of graphs. (English) Zbl 1122.05072
Summary: We present lower and upper bounds for the independence number \(\alpha (G)\) and the clique number \(\omega (G)\) involving the Laplacian eigenvalues of the graph \(G\).

MSC:
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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[1] Chung, F.R.K., Diameters and eigenvalues, J. amer. math. soc., 2, 187-196, (1989) · Zbl 0678.05037
[2] Chung, F.R.K.; Faber, V.; Manteuffel, T.A., An upper bound on the diameter of a graph from eigenvalues, SIAM J. discrete math., 7, 443-457, (1994) · Zbl 0808.05072
[3] Cvetković, D.; Doob, M.; Sachs, H., Spectra of graphs, (1980), Academic Press New York · Zbl 0458.05042
[4] Fiedler, M., Algebraic connectivity of graphs, Czechoslovak math. J., 3, 98, 298-305, (1973) · Zbl 0265.05119
[5] C.D. Godsil, M.W. Newman, Eigenvalue bounds for independent sets, J. Combin. Theory Ser. B, in press · Zbl 1156.05041
[6] Grone, R.; Merris, R., The Laplacian spectrum of a graph (II), SIAM J. discrete math., 7, 221-229, (1994) · Zbl 0795.05092
[7] Haemers, W.H., Interlacing eigenvalues and graphs, Linear algebra appl., 226-228, 593-616, (1995) · Zbl 0831.05044
[8] Mohar, B., Isoperimetric number of graphs, J. combin. theory ser. B, 47, 274-291, (1989) · Zbl 0719.05042
[9] Mohar, B., The Laplacian spectrum of graphs, (), 871-898 · Zbl 0840.05059
[10] Motzkin, T.; Straus, E.G., Maxima for graphs and a new proof of a theorem of Turán, Canad. J. math., 17, 533-540, (1965) · Zbl 0129.39902
[11] Rojo, O.; Soto, R.; Rojo, H., An always non-trivial upper bound for Laplacian graph eigenvalues, Linear algebra appl., 312, 155-159, (2000) · Zbl 0958.05088
[12] Wilf, H.S., Spectral bounds for the clique and independence numbers of graphs, J. combin. theory ser. B, 40, 113-117, (1986) · Zbl 0598.05047
[13] Zhang, X.D.; Luo, R., The spectral radius of triangle-free graphs, Australas. J. combin., 26, 33-39, (2002) · Zbl 1008.05089
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