Eigenvalue bracketing for discrete and metric graphs

[摘要] We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using various 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. (C) 2008 Elsevier Inc. All rights reserved.

[发布日期] 2008-12-15

[关键词] Laplacian;discrete graphs;metric graphs;covering graphs;gaps in the spectrum