Isospectrality for graph laplacians under the change of coupling at graph vertices: Necessary and sufficient conditions

Yulia Ershova; Irina I. Karpenko; Alexander V. Kiselev

doi:10.1112/S0025579314000394

Isospectrality for graph laplacians under the change of coupling at graph vertices: Necessary and sufficient conditions

Yulia Ershova, Irina I. Karpenko, Alexander V. Kiselev

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

Abstract

Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of types δ and δ'. Assuming rational independence of edge lengths, necessary and sufficient conditions for isospectrality of two Laplacians defined on the same graph are derived and scrutinized. It is proved that the spectrum of a graph Laplacian uniquely determines matching conditions for "almost all" graphs.

Original language	English
Pages (from-to)	210-242
Number of pages	33
Journal	Mathematika
Volume	62
Issue number	1
Early online date	16 Jan 2015
DOIs	https://doi.org/10.1112/S0025579314000394
Publication status	Published - 31 Dec 2016

Bibliographical note

Funding information:
The third authors’ work was partially supported by the RFBR, grant no. 12-01-00215-a.

ASJC Scopus subject areas

General Mathematics

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AB - Laplace operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of types δ and δ'. Assuming rational independence of edge lengths, necessary and sufficient conditions for isospectrality of two Laplacians defined on the same graph are derived and scrutinized. It is proved that the spectrum of a graph Laplacian uniquely determines matching conditions for "almost all" graphs.

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Isospectrality for graph laplacians under the change of coupling at graph vertices: Necessary and sufficient conditions

Abstract

Bibliographical note

ASJC Scopus subject areas

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