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Graphs and matrices of maximal energy

Vladimir Nikiforov
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Abstract

Call the sum of the singular values of a matrix A the energy of A. We investigate graphs and matrices of energy close to the maximal one. We prove a conjecture of Koolen and Moulten and give a stability theorem characterizing all square nonnegative matrices and all graphs with energy close to the maximal one. In particular, such graphs are quasi-random.

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Vladimir Nikiforov. 2006-03-30. Graphs and matrices of maximal energy. https://arxiv.org/abs/math/0603725

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