The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions

Author:

Band Ram,Berkolaiko Gregory,Raz Hillel,Smilansky Uzy

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference38 articles.

1. Al-Obeid, O.: On the number of the constant sign zones of the eigenfunctions of a dirichlet problem on a network (graph). Technical report, Voronezh: Voronezh State University, 1992. in Russian, deposited in VINITI 13.04.93, N 938 – B 93. – 8 p

2. Band, R., Berkolaiko, G., Smilansky, U.: Dynamics of nodal points and the nodal count on a family of quantum graphs. Ann. Henri Poincare, pp. 1–40. doi: 10.1007/s00023-011-0124-1 . http://dx.doi.org/10.1007/s00023-011-0124-1

3. Band, R., Oren, I., Smilansky, U.: Nodal domains on graphs — how to count them and why? In Analysis on graphs and its applications, volume 77 of Proc. Sympos. Pure Math., Providence, RI: Amer. Math. Soc., 2008, pp. 5–27

4. Band R., Shapira T., Smilansky U.: Nodal domains on isospectral quantum graphs: the resolution of isospectrality?. J. Phys. A 39(45), 13999–14014 (2006)

5. Berkolaiko G.: A lower bound for nodal count on discrete and metric graphs. Commun. Math. Phys. 278(3), 803–819 (2008)

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