Graph Laplacians and Topology

Pavel Kurasov

doi:10.1007/s11512-007-0059-4

Graph Laplacians and Topology

Pavel Kurasov

Mathematics (Faculty of Engineering)

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

Abstract

Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues.

Original language	English
Pages (from-to)	95-111
Journal	Arkiv för Matematik
Volume	46
Issue number	1
DOIs	https://doi.org/10.1007/s11512-007-0059-4
Publication status	Published - 2008

Subject classification (UKÄ)

Mathematical Sciences

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10.1007/s11512-007-0059-4

http://www.springerlink.com/content/d428304272rxp17h/fulltext.pdf

Cite this

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title = "Graph Laplacians and Topology",

abstract = "Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues.",

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AB - Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same characteristics are determined by the scattering data consisting of the scattering matrix and the discrete eigenvalues.

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JO - Arkiv för Matematik

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Graph Laplacians and Topology

Abstract

Subject classification (UKÄ)

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