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Graph Laplacians and topology

Pavel Kurasov Department of Mathematics LTH, Lund University

TBD mathscidoc:1701.333122

Arkiv for Matematik, 46, (1), 95-111, 2006.6
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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@inproceedings{pavel2006graph,
  title={Graph Laplacians and topology},
  author={Pavel Kurasov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203621771762931},
  booktitle={Arkiv for Matematik},
  volume={46},
  number={1},
  pages={95-111},
  year={2006},
}
Pavel Kurasov. Graph Laplacians and topology. 2006. Vol. 46. In Arkiv for Matematik. pp.95-111. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203621771762931.
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