Nodal domains on graphs - How to count them and why?
arXiv:0711.3416
Abstract
The purpose of the present manuscript is to collect known results and present some new ones relating to nodal domains on graphs, with special emphasize on nodal counts. Several methods for counting nodal domains will be presented, and their relevance as a tool in spectral analysis will be discussed.
Some corrections according to the referees report were made
References in corpus (7)
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Nodal domains statistics - a criterion for quantum chaos
- Percolation model for nodal domains of chaotic wave functions
- Nodal domains on quantum graphs
- Can one count the shape of a drum?
- On the Number of Nodal Domains of Random Spherical Harmonics
- Counting nodal domains
Cited by in corpus (5)
- Quantum graphs: an introduction and a brief survey
- Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count
- Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs
- Isospectral discrete and quantum graphs with the same flip counts and nodal counts
- Many nodal domains in random regular graphs