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 identical, with the possible exception of the multiplicity of the eigenvalue zero. 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, again with the possible exception of the eigenvalue zero.
- Pub Date:
- March 2012
- Mathematics - Spectral Theory
- This article has now been published but unfortunately the published version contains an error in the treatment of the eigenvalue zero. The version here is the corrected version