Displaying similar documents to “Lower bounds for the spectral norm.”

Unified Spectral Bounds on the Chromatic Number

Clive Elphick, Pawel Wocjan (2015)

Discussiones Mathematicae Graph Theory

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One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn. We recently generalised this bound to include all eigenvalues of the adjacency matrix. In this paper, we further generalize these results to include all eigenvalues of the adjacency, Laplacian and signless Laplacian matrices. The various known bounds...

New bounds for the minimum eigenvalue of 𝓜-tensors

Jianxing Zhao, Caili Sang (2017)

Open Mathematics

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A new lower bound and a new upper bound for the minimum eigenvalue of an 𝓜-tensor are obtained. It is proved that the new lower and upper bounds improve the corresponding bounds provided by He and Huang (J. Inequal. Appl., 2014, 2014, 114) and Zhao and Sang (J. Inequal. Appl., 2016, 2016, 268). Finally, two numerical examples are given to verify the theoretical results.

New bounds for the minimum eigenvalue ofM-matrices

Feng Wang, Deshu Sun (2016)

Open Mathematics

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Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.