# MathSciDoc: An Archive for Mathematician ∫

#### 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 [
@inproceedings{yong2013nodal,