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arXiv · 1307.3226

Nodal geometry of graphs on surfaces

Yong Lin·Gabor Lippner·Dan Mangoubi·Shing-Tung Yau
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Abstract

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 $n$th Laplacian eigenvalue is at most $2\left[ 6(n-1) + 15(2g-2) \right]^2$. Our results hold for any Schrödinger operator, not just the Laplacian.

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Yong Lin, Gabor Lippner, Dan Mangoubi, Shing-Tung Yau. 2013-07-11. Nodal geometry of graphs on surfaces. https://doi.org/10.3934/dcds.2010.28.1291

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