Eigenvalue Bracketing for Discrete and Metric Graphs Articles uri icon

publication date

  • December 2008

start page

  • 806

end page

  • 833


  • 2


  • 348

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813


  • 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.