A Graph Spectral Flow for Computing Nodal Deficiencies
Combinatorics
2021-03-08 v2 Spectral Theory
Abstract
In this paper we propose a spectral flow for graph Laplacians, and prove that it counts the number of nodal domains for a given Laplace eigenvector. This extends work done for Laplacians on to the graph setting. We mention some open problems relating the topology of a graph to the analytic behaviour of its Laplace eigenvectors, and include numerical examples illustrating our flow.
Cite
@article{arxiv.2008.10684,
title = {A Graph Spectral Flow for Computing Nodal Deficiencies},
author = {Wesley Hamilton},
journal= {arXiv preprint arXiv:2008.10684},
year = {2021}
}