Answers are grounded in this paper and cite their sources.
This paper demonstrates the Brouwer conjecture holds for graphs with sufficient vertices, suggesting implications for quivers.
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.
No takes yet. Share an insight, caveat, or question.
Oliver Knill (2025) studied this question.
Synapse has enriched 8 closely related papers on similar clinical questions. Consider them for comparative context: