Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

@article{Berkolaiko2010DependenceOT,
  title={Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths},
  author={Gregory Berkolaiko and Peter Kuchment},
  journal={arXiv: Mathematical Physics},
  year={2010}
}
We study the dependence of the quantum graph Hamiltonian, its resolvent, and its spectrum on the vertex conditions and graph edge lengths. In particular, several results on the interlacing (bracketing) of the spectra of graphs with different vertex conditions are obtained and their applications are discussed. 
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