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Abstract: We develop eigenvalue estimates for the Laplacians on discrete and metricgraphs using different types of boundary conditions at the vertices of themetric graph. Via an explicit correspondence of the equilateral metric anddiscrete graph spectrum also in the ``exceptional- values of the metric graphcorresponding to the Dirichlet spectrum we carry over these estimates from themetric graph Laplacian to the discrete case. We apply the results to coveringgraphs and present examples where the covering graph Laplacians have spectralgaps.



Autor: Olaf Post, Fernando Lledo

Fuente: https://arxiv.org/







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