Abstract
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere aside from a sufficiently sparse set, then the eigenvalue-spectra and the length-spectra of the two quantum graphs are completely identical. Similarly, if their length-spectra agree everywhere aside from a sufficiently sparse set, then the quantum graphs have the same eigenvalue-spectrum and length-spectrum.
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This work was supported by a grant from EPSRC (grant EP/G021287/1).
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Communicated by Jiaping Wang.
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Rueckriemen, R. Quasi-isospectrality on Quantum Graphs. J Geom Anal 25, 306–316 (2015). https://doi.org/10.1007/s12220-013-9428-3
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DOI: https://doi.org/10.1007/s12220-013-9428-3