Remarks on the Brouwer Conjecture
Combinatorics
2025-08-14 v2 Discrete Mathematics
Abstract
The Brouwer conjecture (BC) in spectral graph theory claims that the sum of the largest k Kirchhoff eigenvalues of a graph are bounded above by the number m of edges plus k(k+1)/2. We show that (BC) holds for all graphs with n vertices if n is larger or equal than 4 times the square of the maximal vertex degree. We also note that (BC) for graphs implies (BC) for quivers.
Cite
@article{arxiv.2508.07550,
title = {Remarks on the Brouwer Conjecture},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:2508.07550},
year = {2025}
}
Comments
15 pages 3 figures, corrected and more references