Graphs and matrices of maximal energy
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0603725,
title = {Graphs and matrices of maximal energy},
author = {Vladimir Nikiforov},
journal= {arXiv preprint arXiv:math/0603725},
year = {2007}
}