2008/04/07 by Olaf Post, Post, Olaf, Fernando Lledó +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Graph theory and applications #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.0804.1076
openalex publication_date 2008/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph spectrum (also in the ``exceptional'' values of the metric graph corresponding to the Dirichlet spectrum) we carry over these estimates from the metric graph Laplacian to the discrete case. We apply the results to covering graphs and present examples where the covering graph Laplacians have spectral gaps.