English

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}
}
R2 v1 2026-07-22T17:33:33.830Z