English

Sums of squares of eigenvalues and the vector chromatic number

Combinatorics 2023-08-10 v1

Abstract

In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided by the vector chromatic number, resolving a conjecture by Wocjan, Elphick and Anekstein (2018).

Keywords

Cite

@article{arxiv.2308.04475,
  title  = {Sums of squares of eigenvalues and the vector chromatic number},
  author = {Gabriel Coutinho and Thomás Jung Spier},
  journal= {arXiv preprint arXiv:2308.04475},
  year   = {2023}
}