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2013, Mathematical surveys and monographs, ISBN 9780821892114, Volume 186, xiii, 270
Book
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 1, pp. 803 - 818
We prove that after an arbitrarily small adjustment of edge lengths, the spectrum of a compact quantum graph with -type vertex conditions can be simple. We... 
Quantum graphs | Zeros of eigenfunctions | Simple spectrum
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 8/2018, Volume 108, Issue 8, pp. 1825 - 1835
We construct rich families of Schrödinger operators on symmetric graphs, both quantum and combinatorial, whose spectral degeneracies are persistently larger... 
Graph spectra | 05C50 | Combinatorial Laplacian | 34B45 | Theoretical, Mathematical and Computational Physics | Complex Systems | Metric graphs | Physics | Geometry | 20C35 | Irreducible representations | Degenerate eigenvalues | Group Theory and Generalizations | PHYSICS, MATHEMATICAL
Journal Article
Analysis and PDE, ISSN 2157-5045, 2013, Volume 6, Issue 5, pp. 1213 - 1233
We establish a connection between the stability of an eigenvalue under a magnetic perturbation and the number of zeros of the corresponding eigenfunction.... 
Nodal count | Discrete laplace operator | Discrete magnetic schrödinger operator | nodal count | MATHEMATICS | discrete Laplace operator | MATHEMATICS, APPLIED | NUMBER | ELECTRONS | DISCRETE | DOMAINS | discrete magnetic Schrodinger operator
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2019, Volume 372, Issue 7, pp. 5153 - 5197
We present a systematic collection of spectral surgery principles for the Laplacian on a compact metric graph with any of the usual vertex conditions (natural,... 
MATHEMATICS | EIGENVALUES | bounds on spectral gaps | Quantum graphs | spectral geometry of quantum graphs | ALGEBRAIC CONNECTIVITY | GROUND-STATES | Mathematics - Spectral Theory | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 2019, Volume 109, Issue 7, pp. 1611 - 1623
It has been recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the... 
Nodal sets | Spectral indices | Nodal domains | Dirichlet-to-Neumann map | PHYSICS, MATHEMATICAL
Journal Article
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 01/2014, Volume 372, Issue 2007, p. 20120522
We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros phi of the nth eigenfunction of the Schrdinger operator on a quantum... 
Magnetic Schrodinger operator | Nodal count | Quantum graphs | Magnetic-nodal connection | Zeros of eigenfunctions | nodal count | quantum graphs | zeros of eigenfunctions | MULTIDISCIPLINARY SCIENCES | magnetic Schrodinger operator | magnetic-nodal connection | DOMAINS | 1008 | magnetic Schrödinger operator | 120
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 08/2017, Volume 50, Issue 36, p. 365201
We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge... 
spectral gap | quantum graph | Sturm-Liouville problem | graph | Laplacian | spectral geometry | EIGENVALUES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Mathematics - Spectral Theory | Fysik | Physical Sciences | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 12/2015, Volume 56, Issue 12, p. 122111
We study the nodal count of the so-called bi-dendral graphs and show that it exhibits an anomaly: the nodal surplus is never equal to 0 or beta, the first... 
EIGENVALUES | POINTS | PHYSICS, MATHEMATICAL | SPECTRAL STATISTICS | OPERATORS | DOMAINS | FLUXES | QUANTUM GRAPHS
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 12/2012, Volume 22, Issue 6, pp. 1517 - 1540
The paper addresses the nodal count (i.e., the number of nodal domains) for eigenfunctions of Schrödinger operators with Dirichlet boundary conditions in... 
Analysis | Mathematics | MATHEMATICS | GENERIC PROPERTIES | RESOLVING ISOSPECTRAL DRUMS | DOMAINS | HADAMARD VARIATIONAL FORMULA
Journal Article
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