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Nodal geometry of graphs on surfaces

Yong Lin Gbor Lippner Dan Mangoubi Shing-Tung Yau

Convex and Discrete Geometry mathscidoc:1912.43645

arXiv preprint arXiv:1307.3226, 2013.7
We prove two mixed versions of the Discrete Nodal Theorem of Davies et. al.[3] for bounded degree graphs, and for three-connected graphs of fixed genus g . Using this we can show that for a three-connected graph satisfying a certain volume-growth condition, the multiplicity of the g th Laplacian eigenvalue is at most $2\left [
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@inproceedings{yong2013nodal,
  title={Nodal geometry of graphs on surfaces},
  author={Yong Lin, Gbor Lippner, Dan Mangoubi, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204711554393209},
  booktitle={arXiv preprint arXiv:1307.3226},
  year={2013},
}
Yong Lin, Gbor Lippner, Dan Mangoubi, and Shing-Tung Yau. Nodal geometry of graphs on surfaces. 2013. In arXiv preprint arXiv:1307.3226. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204711554393209.
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