The nodal count {0,1,2,3,…} implies the graph is a tree

DOI10.1098/rsta.2012.0504zbMath1352.34019arXiv1212.6710OpenAlexW3123681079WikidataQ37399873 ScholiaQ37399873MaRDI QIDQ2945348

Ram Band

Publication date: 9 September 2015

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6710

zbMATH Keywords

Sturm-Liouville problemsinverse spectral problemsquantum graphsnodal data

Mathematics Subject Classification ID

Inverse problems involving ordinary differential equations (34A55) Boundary value problems on graphs and networks for ordinary differential equations (34B45)

Related Items (16)

Isospectral discrete and quantum graphs with the same flip counts and nodal counts ⋮ Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph ⋮ Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮ A theory of spectral partitions of metric graphs ⋮ Nodal statistics on quantum graphs ⋮ Complex patterns in wave functions: drums, graphs and disorder ⋮ Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions ⋮ Minimizing optimal transport for functions with fixed-size nodal sets ⋮ Neumann domains on quantum graphs ⋮ On the hot spots of quantum graphs ⋮ Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold ⋮ Graphs and their real eigenvectors ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ On fully supported eigenfunctions of quantum graphs ⋮ On the nodal structure of nonlinear stationary waves on star graphs ⋮ Nonlinear Sturm oscillation: From the interval to a star

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