2020/08/24 by Wesley Hamilton, Hamilton, Wesley
Mathematics · Computer Science · #Graph theory and applications #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2008.10684
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 ℝn 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.