Nodal geometry of graphs on surfaces
Combinatorics
2015-12-02 v1 Spectral Theory
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 . Using this we can show that for a three-connected graph satisfying a certain volume-growth condition, the multiplicity of the th Laplacian eigenvalue is at most . Our results hold for any Schr\"odinger operator, not just the Laplacian.
Cite
@article{arxiv.1307.3226,
title = {Nodal geometry of graphs on surfaces},
author = {Yong Lin and Gabor Lippner and Dan Mangoubi and Shing-Tung Yau},
journal= {arXiv preprint arXiv:1307.3226},
year = {2015}
}