2022/05/23 by Oliver Knill, Knill, Oliver · 1 citation
Computer Science · Mathematics · #05Cxx #05Exx #68Rxx #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.2205.10968
openalex publication_date 2022/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that each eigenvalue l(k) of the Kirchhoff Laplacian K of a graph or quiver is bounded above by d(k)+d(k-1) for all k in 1,...,n. Here l(1),...,l(n) is a non-decreasing list of the eigenvalues of K and d(1),..,d(n) is a non-decreasing list of vertex degrees with the additional assumption d(0)=0. We also prove that in general the weak Brouwer-Haemers lower bound d(k) + (n-k) holds for all eigenvalues l(k) of the Kirchhoff matrix of a quiver.