Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count

DOI10.1088/1751-8113/45/16/165203zbMath1242.05159arXiv1110.3802OpenAlexW2149084252MaRDI QIDQ2888585

Uzy Smilansky, Gregory Berkolaiko, Hillel Raz

Publication date: 1 June 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.3802

zbMATH Keywords

discrete Schrödinger operatornodal deficiency for generic eigenvectors

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (8)

Isospectral discrete and quantum graphs with the same flip counts and nodal counts ⋮ Courant-sharp eigenvalues of Neumann 2-rep-tiles ⋮ The nodal count {0,1,2,3,…} implies the graph is a tree ⋮ Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions ⋮ Stability of spectral partitions and the Dirichlet-to-Neumann map ⋮ Rayleigh estimates for differential operators on graphs ⋮ Critical partitions and nodal deficiency of billiard eigenfunctions ⋮ The number of nodal domains on quantum graphs as a stability index of graph partitions

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