## DEPENDENCE OF THE SPECTRUM OF A QUANTUM GRAPH ON VERTEX CONDITIONS AND EDGE LENGTHS

### BibTeX

@MISC{Berkolaiko_dependenceof,

author = {Gregory Berkolaiko and Peter Kuchment},

title = {DEPENDENCE OF THE SPECTRUM OF A QUANTUM GRAPH ON VERTEX CONDITIONS AND EDGE LENGTHS},

year = {}

}

### OpenURL

### Abstract

Abstract. 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. 1.

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Citation Context ...nd study their interlacing properties. Eigenvalue interlacing (or bracketing) is a powerful tool in spectral theory with such well-known applications as the derivation of the asymptotic Weyl law, see =-=[5]-=-. In the graph setting, it allows one to estimate eigenvalue of a given graph via the eigenvalues of its subgraphs, which may be easier to calculate. Interlacing results on graphs have already been us... |

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