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}
}