zbMath1318.81005MaRDI QIDQ4904449
Gregory Berkolaiko, Peter A. Kuchment
Publication date: 30 January 2013
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Distinguishing cospectral quantum graphs by scattering ⋮
Kagome network with vertex coupling of a preferred orientation ⋮
The heat kernel on the diagonal for a compact metric graph ⋮
Index theorems for graph-parametrized optimal control problems ⋮
Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮
Spectral properties of singular Sturm-Liouville operators via boundary triples and perturbation theory ⋮
Nonlinear dynamics of modulated waves on graphene like quantum graphs ⋮
Trace formula of the differential operator with delays on a quantum graph ⋮
Resolvent expansions for self‐adjoint operators via boundary triplets ⋮
Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons ⋮
Unnamed Item ⋮
Minimizing optimal transport for functions with fixed-size nodal sets ⋮
Controllability for the wave equation on graph with cycle and delta-prime vertex conditions ⋮
Ground states for the NLS equation with combined local nonlinearities on noncompact metric graphs ⋮
Spectral minimal partitions of unbounded metric graphs ⋮
Ground state and orbital stability for the NLS equation on a general starlike graph with potentials ⋮
Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation ⋮
Laplacians on infinite graphs: discrete vs. continuous ⋮
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown ⋮
Matrix functions in network analysis ⋮
Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge ⋮
Synthesis of a quantum tree Weyl matrix ⋮
Surgery transformations and spectral estimates of \(\delta\) beam operators ⋮
A nonlinear Klein–Gordon equation on a star graph ⋮
UNIQUE SOLVABILITY OF IBVP FOR PSEUDO-SUBDIFFUSION EQUATION WITH HILFER FRACTIONAL DERIVATIVE ON A METRIC GRAPH ⋮
Closed form expressions for the Green’s function of a quantum graph—a scattering approach ⋮
Recovery of a potential on a quantum star graph from Weyl's matrix ⋮
Construction of self‐adjoint differential operators with prescribed spectral properties ⋮
Graph‐like spaces approximated by discrete graphs and applications ⋮
Localized eigenvectors on metric graphs ⋮
Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮
Magnetic square lattice with vertex coupling of a preferred orientation ⋮
Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations ⋮
Optimal control problems of parabolic fractional Sturm-Liouville equations in a star graph ⋮
Normalized solutions of L 2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities ⋮
Schrödinger operators with guided potentials on periodic graphs ⋮
Ornstein-Uhlenbeck semigroups on star graphs ⋮
On the parabolic Cauchy problem for quantum graphs with vertex noise ⋮
Quantum graphs: Coulomb-type potentials and exactly solvable models ⋮
On the discrete spectrum of a one-dimensional discrete Schrödinger operator with a perturbation of rank one ⋮
On the Density of Eigenvalues on Periodic Graphs ⋮
Blow-up on metric graphs and Riemannian manifolds ⋮
Time evolution and the Schrödinger equation on time dependent quantum graphs * ⋮
D^²=H+¼ with point interactions ⋮
On the existence of bound states of a system of two fermions on the two-dimensional cubic lattice ⋮
Self‐adjoint and Markovian extensions of infinite quantum graphs ⋮
Classification and stability of positive solutions to the NLS equation on the T -metric graph ⋮
Discrete honeycombs, rational edges, and edge states ⋮
Efficient Mediated Quantum Secret Sharing Protocol in a Restricted Quantum Environment ⋮
From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮
Edge connectivity and the spectral gap of combinatorial and quantum graphs ⋮
Spectral stability of shifted states on star graphs ⋮
Visibility of quantum graph spectrum from the vertices ⋮
Maximal scarring for eigenfunctions of quantum graphs ⋮
Ground States of the L 2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph ⋮
A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs ⋮
Strong Isoperimetric Inequality for Tessellating Quantum Graphs ⋮
Spectral Monotonicity for Schrödinger Operators on Metric Graphs ⋮
The Landau Hamiltonian with δ-potentials supported on curves ⋮
On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs ⋮
Spectral estimates for Schrödinger operators on periodic discrete graphs ⋮
Orbital instability of standing waves for NLS equation on star graphs ⋮
Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum ⋮
Gluing graphs and the spectral gap: a Titchmarsh–Weyl matrix-valued function approach ⋮
Generic properties of dispersion relations for discrete periodic operators ⋮
Parameter dependent differential operators on graphs and their applications ⋮
Scattering on periodic metric graphs ⋮
Normalized solutions for the Kirchhoff equation on noncompact metric graphs * ⋮
On the distribution of energy of localized solutions of the Schrödinger equation that propagate along symmetric quantum graphs ⋮
Ring chains with vertex coupling of a preferred orientation ⋮
Schrodinger Operators on a Zigzag Supergraphene-Based Carbon Nanotube ⋮
Optimal Control Problems Driven by Time-Fractional Diffusion Equations on Metric Graphs: Optimality System and Finite Difference Approximation ⋮
Edge switching transformations of quantum graphs—a scattering approach ⋮
On ergodic diffusions on continuous graphs whose centered resolvent admits a trace ⋮
Elliptic differential operators on infinite graphs with general conditions on vertices ⋮
Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity ⋮
Localization and landscape functions on quantum graphs ⋮
Spectral asymptotics of the Laplacian on Platonic solids graphs ⋮
Unnamed Item ⋮
Branching Random Walks on $Z^d$ with Periodic Branching Sources ⋮
Surgery principles for the spectral analysis of quantum graphs ⋮
Solvable models of interacting 𝑛-particle systems on quantum graphs ⋮
Nonlinear Sturm oscillation: From the interval to a star ⋮
Existence of the ground state for the NLS with potential on graphs ⋮
Fredholm theory of differential operators on periodic graphs ⋮
Optimization of the lowest eigenvalue for leaky star graphs ⋮
The Schrödinger equation on a star-shaped graph under general coupling conditions ⋮
One-sided Diophantine approximations ⋮
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs ⋮
Quantum graphs via exercises ⋮
Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals ⋮
Non-self-adjoint graphs ⋮
Magnetic ring chains with vertex coupling of a preferred orientation ⋮
Cantor spectra of magnetic chain graphs ⋮
Periodic quantum graphs with predefined spectral gaps ⋮
Spectrum of a non-selfadjoint quantum star graph ⋮
Complete dynamical evaluation of the characteristic polynomial of binary quantum graphs ⋮
On extremal eigenvalues of the graph Laplacian * ⋮
Effective numerical method of spectral analysis of quantum graphs ⋮
A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs ⋮
Standing waves on quantum graphs ⋮
Quantum walk on a comb with infinite teeth ⋮
PT-symmetric quantum graphs ⋮
Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs ⋮
Isospectral discrete and quantum graphs with the same flip counts and nodal counts ⋮
Spectral properties of quantum circulant graphs ⋮
Bound states of the NLS equation on metric graphs with localized nonlinearities ⋮
The Maslov and Morse indices for Schrödinger operators on \([0,1\)] ⋮
Spectral band structure of periodic Schrödinger operators with two potentials on the degenerate zigzag nanotube ⋮
Concrete method for recovering the Euler characteristic of quantum graphs ⋮
On reflectionless equi-transmitting matrices ⋮
Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph ⋮
Unnamed Item ⋮
Some Remarks on the Krein-von Neumann Extension of Different Laplacians ⋮
Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮
Threshold of discrete Schrödinger operators with delta potentials on n-dimensional lattice ⋮
Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples ⋮
Scattering theory for the matrix Schrödinger operator on the half line with general boundary conditions ⋮
Uncertainty principle for discrete Schrödinger evolution on graphs ⋮
A Gelfand-Levitan trace formula for generic quantum graphs ⋮
On the quotient quantum graph with respect to the regular representation ⋮
Bilinear quantum systems on compact graphs: well-posedness and global exact controllability ⋮
Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length ⋮
Doubly nonlinear Schrödinger ground states on metric graphs ⋮
A theory of spectral partitions of metric graphs ⋮
On inverse topology problem for Laplace operators on graphs ⋮
Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover ⋮
Optimal Mass Transport on Metric Graphs ⋮
Forcing operators on star graphs applied for the cubic fourth order Schrödinger equation ⋮
Exact controllability to eigensolutions of the bilinear heat equation on compact networks ⋮
Continuum limit of the lattice quantum graph Hamiltonian ⋮
The Cheeger cut and Cheeger problem in metric graphs ⋮
Dirac operators on infinite quantum graphs ⋮
The number of eigenvalues of the matrix Schrödinger operator on the half line with general boundary conditions ⋮
Method for solving inverse spectral problems on quantum star graphs ⋮
Scattering properties of two singularly interacting particles on the half-line ⋮
Stability results of some first order viscous hyperbolic systems ⋮
Quantum ergodicity for large equilateral quantum graphs ⋮
Periodic quantum graphs from the Bethe–Sommerfeld perspective ⋮
An integrable matrix NLS equation on star graph and symmetry-dependent connection conditions of vertex ⋮
Multi-peak solutions for the Schnakenberg model with heterogeneity on star shaped graphs ⋮
Eigenvalue estimates for the Laplacian on a metric tree ⋮
Inverse problems for the Dirac operator on a star graph ⋮
Laplacians with Point Interactions—Expected and Unexpected Spectral Properties ⋮
The matrix nonlinear Schrödinger equation with a potential ⋮
Computation and learning in high dimensions. Abstracts from the workshop held August 1--7, 2021 (hybrid meeting) ⋮
Functional-differential operators on geometrical graphs with global delay and inverse spectral problems ⋮
Quantum graphs: PT-symmetry and reflection symmetry of the spectrum ⋮
Generic asymptotics of resonance counting function for Schrödinger point interactions ⋮
Modern results in the spectral analysis for a class of integral-difference operators and application to physical processes ⋮
Inverse problem for integral-difference operators on graphs ⋮
Quantum graph in a magnetic field and resonance states completeness ⋮
Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology ⋮
Upper bound for the diameter of a tree in the quantum graph theory ⋮
Peaked and Low Action Solutions of NLS Equations on Graphs with Terminal Edges ⋮
An elementary introduction to quantum graphs ⋮
Delay-time distribution in the scattering of time-narrow wave packets (II)—quantum graphs ⋮
Superdiffusive fractional in time Schrödinger equations: a unifying approach to superdiffusive waves ⋮
Exactly solvable interacting two-particle quantum graphs ⋮
Can one hear the spanning trees of a quantum graph? ⋮
Many-Particle Quantum Graphs: A Review ⋮
Kreı̆n Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One ⋮
Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics ⋮
The Maslov and Morse indices for system Schroedinger operators on \mathBB{R} ⋮
Numerical estimates of the essential spectra of quantum graphs with delta-interactions at vertices ⋮
On the eigenvalues for a weighted p-Laplacian operator on metric graphs ⋮
An index theorem for Schrödinger operators on metric graphs ⋮
Nonlinear Dirac Equation on Graphs with Localized Nonlinearities: Bound States and Nonrelativistic Limit ⋮
A Differential Model for Growing Sandpiles on Networks ⋮
On the Spectrum Discreteness for the Magnetic Schrödinger Operator on Quantum Graphs ⋮
Schrödinger operators on graphs: Symmetrization and Eulerian cycles ⋮
Estimates of bands for Laplacians on periodic equilateral metric graphs ⋮
Expansion in generalized eigenfunctions for Laplacians on graphs and metric measure spaces ⋮
A family of quantum graph vertex couplings interpolating between different symmetries ⋮
Trace formulas for Schrödinger operators on star graphs with general matching conditions ⋮
On the existence of bound states in asymmetric leaky wires ⋮
\(n\)-particle quantum statistics on graphs ⋮
Unnamed Item ⋮
Inverse eigenvalue problem for a simple star graph ⋮
Spectral Gap for Complete Graphs: Upper and Lower Estimates ⋮
Instability of Bose-Einstein condensation into the one-particle ground state on quantum graphs under repulsive perturbations ⋮
Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media ⋮
An overview of periodic elliptic operators ⋮
Spectral continuity for aperiodic quantum systems: Applications of a folklore theorem ⋮
Laplacians on bipartite metric graphs ⋮
Spectral optimization for singular Schrödinger operators ⋮
Lower estimates on eigenvalues of quantum graphs ⋮
Local Transparent Boundary Conditions for Wave Propagation in Fractal Trees (II). Error and Complexity Analysis ⋮
A Fermi golden rule for quantum graphs ⋮
Zeta functions of the Dirac operator on quantum graphs ⋮
Local minimizers in absence of ground states for the critical NLS energy on metric graphs ⋮
Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphs ⋮
Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions ⋮
Sharp diameter bound on the spectral gap for quantum graphs ⋮
Linear instability criterion for the Korteweg–de Vries equation on metric star graphs ⋮
Stable Computation of Generalized Matrix Functions via Polynomial Interpolation ⋮
Asymptotic Formulae for Weight Numbers of the Sturm – Liouville Boundary Problem on a Star-shaped Graph ⋮
Hidden symmetries in non-self-adjoint graphs ⋮
Ground States for the NLS Equation with Combined Nonlinearities on Noncompact Metric Graphs ⋮
The extremals of Minkowski's quadratic inequality ⋮
Infinite quantum graphs ⋮
Exact controllability of the wave equation on graphs ⋮
On equi-transmitting matrices ⋮
Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮
A Calderón type inverse problem for tree graphs ⋮
Gradient flow approach to the calculation of stationary states on nonlinear quantum graphs ⋮
Numerical simulations on nonlinear quantum graphs with the GraFiDi library ⋮
Homogenization of stiff inclusions through network approximation ⋮
Tight-binding reduction and topological equivalence in strong magnetic fields ⋮
A matrix Schrödinger approach to focusing nonlinear Schrödinger equations with nonvanishing boundary conditions ⋮
Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling ⋮
Validity of the NLS approximation for periodic quantum graphs ⋮
Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph ⋮
Schrödinger operators on a periodically broken zigzag carbon nanotube ⋮
Reaction-diffusion on metric graphs: from 3D to 1D ⋮
The Maslov index for Lagrangian pairs on \(\mathbb{R}^{2 n}\) ⋮
Stability of standing waves for NLS-log equation with \(\delta\)-interaction ⋮
Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮
Convergence of spectra of uniformly fattened open book structures ⋮
Optimal potentials for quantum graphs ⋮
Localized asymptotic solution of a variable-velocity wave equation on the simplest decorated graph ⋮
Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs ⋮
Well-posedness of systems of 1-D hyperbolic partial differential equations ⋮
New trace formulae for Sturm-Liouville operators on the Lasso-graph ⋮
\(L^2\)-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features ⋮
Recovering the shape of a quantum graph ⋮
Spectral determinants and an Ambarzumian type theorem on graphs ⋮
The inverse problem for differential pencils on a star-shaped graph with mixed spectral data ⋮
Electromagnetic Schrödinger operators on periodic graphs with general conditions at vertices ⋮
Asymptotics of the trace of the resolvent of the Laplace operator on a metric graph with arbitrary boundary conditions ⋮
Gaps in the spectrum of a cuboidal periodic lattice graph ⋮
Reaction-diffusion equations on complex networks and Turing patterns, via \(p\)-adic analysis ⋮
Least energy solutions to semi-linear elliptic problems on metric graphs ⋮
Threshold analysis of the three dimensional lattice Schrödinger operator with non-local potential ⋮
Transparent boundary conditions for wave propagation in fractal trees: convolution quadrature approach ⋮
Partial inverse problems for Dirac operators on star graphs ⋮
An example of unitary equivalence between self-adjoint extensions and their parameters ⋮
Topological bulk-edge effects in quantum graph transport ⋮
On a model graph with a loop and small edges. Holomorphy property of resolvent ⋮
Standing waves on a flower graph ⋮
On the sharp effect of attaching a thin handle on the spectral rate of convergence ⋮
Mini-workshop: Self-adjoint extensions in new settings. Abstracts from the mini-workshop held October 6--12, 2019 ⋮
Continuum Schrödinger operators for sharply terminated graphene-like structures ⋮
Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph ⋮
The essential spectrum of the discrete Laplacian on Klaus-sparse graphs ⋮
Non-compact quantum graphs with summable matrix potentials ⋮
\(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮
On the nonlinear Dirac equation on noncompact metric graphs ⋮
Degenerate band edges in periodic quantum graphs ⋮
Concentration phenomena on \(Y\)-shaped metric graph for the Gierer-Meinhardt model with heterogeneity ⋮
The semiclassical limit on a star-graph with Kirchhoff conditions ⋮
Transparent quantum graphs ⋮
Neumann domains on quantum graphs ⋮
Random evolution equations: well-posedness, asymptotics, and applications to graphs ⋮
Quantum graphs: self-adjoint, and yet exhibiting a nontrivial \(\mathcal{PT}\)-symmetry ⋮
Boundary null-controllability of 1-D coupled parabolic systems with Kirchhoff-type conditions ⋮
On the hot spots of quantum graphs ⋮
Singular Schrödinger operators with prescribed spectral properties ⋮
Multi-pulse edge-localized states on quantum graphs ⋮
On the variance of the particle number of a supercritical branching random walk on periodic graphs ⋮
Quantum graphs on radially symmetric antitrees ⋮
Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees ⋮
Maximal quasi-accretive Laplacians on finite metric graphs ⋮
Asymptotics of semigroups generated by operator matrices ⋮
Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold ⋮
On the quantum graph spectra of graphyne nanotubes ⋮
The Maslov and Morse indices for Sturm-Liouville systems on the half-line ⋮
Population dynamics in river networks ⋮
Construction of breather solutions for nonlinear Klein-Gordon equations on periodic metric graphs ⋮
On the decomposition of the Laplacian on metric graphs ⋮
Quantum graphs with summable matrix potentials ⋮
Asymptotically isospectral quantum graphs and generalised trigonometric polynomials ⋮
A note on sign-changing solutions to the NLS on the double-bridge graph ⋮
An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity ⋮
Soliton and breather splitting on star graphs from tricrystal Josephson junctions ⋮
Nonlinear Schrödinger equation with growing potential on infinite metric graphs ⋮
Limits of quantum graph operators with shrinking edges ⋮
Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge ⋮
Convex and quasiconvex functions in metric graphs ⋮
Analyticity of resolvents of elliptic operators on quantum graphs with small edges ⋮
A convection-diffusion model on a star-shaped graph ⋮
On the multilevel internal structure of the asymptotic distribution of resonances ⋮
Upper eigenvalue bounds for the Kirchhoff Laplacian on embedded metric graphs ⋮
On multiplicity of eigenvalues in quantum graph theory ⋮
Nonlinear dispersive equations: classical and new frameworks ⋮
Wave propagation in fractal trees. Mathematical and numerical issues ⋮
Mass-constrained ground states of the stationary NLSE on periodic metric graphs ⋮
A note on Kazdan-Warner equation on networks ⋮
Scale invariant effective Hamiltonians for a graph with a small compact core ⋮
Approximations of metric graphs by thick graphs and their Laplacians ⋮
Gap sets for the spectra of regular graphs with minimum spectral gap ⋮
Taylor series for resolvents of operators on graphs with small edges ⋮
Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition ⋮
Zero modes of quantum graph Laplacians and an index theorem ⋮
On torsional rigidity and ground-state energy of compact quantum graphs ⋮
Spectrum of a dilated honeycomb network ⋮
Controllability for Schrödinger type system with mixed dispersion on compact star graphs ⋮
Entanglement and separability of graph Laplacian quantum states ⋮
Fokker-Planck equation on metric graphs ⋮
Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy ⋮
Spectral band structure of periodic Schrödinger operators on a generalized degenerate zigzag nanotube ⋮
The Maslov index and spectral counts for linear Hamiltonian systems on \([0, 1\)] ⋮
Optimal Dirichlet control of partial differential equations on networks ⋮
Sobolev type inequalities for compact metric graphs ⋮
Asymptotics of the number of endpoints of a random walk on a certain class of directed metric graphs ⋮
\(\mathcal{RT}\)-symmetric Laplace operators on star graphs: real spectrum and self-adjointness ⋮
``Graph paper trace characterizations of functions of finite energy ⋮ Threshold phenomena and existence results for NLS ground states on metric graphs ⋮ Higher-order operators on networks: hyperbolic and parabolic theory ⋮ On the sharpness of spectral estimates for graph Laplacians ⋮ Quantum ergodicity for quantum graphs without back-scattering ⋮ Bogoliubov de Gennes equation on metric graphs ⋮ Spectral estimates for infinite quantum graphs ⋮ On vertex conditions for elastic systems ⋮ Airy-type evolution equations on star graphs ⋮ Upper bounds of the eigenvalues related to a weighted fractional \(p\)-Laplacian on metric graphs ⋮ On the spectral gap of a quantum graph ⋮ Wavelet analysis on symbolic sequences and two-fold de Bruijn sequences ⋮ Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph ⋮ On the lack of bound states for certain NLS equations on metric graphs ⋮ Essential spectrum of Schrödinger operators on periodic graphs ⋮ Spectra of semi-infinite quantum graph tubes ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ On the orbital instability of excited states for the NLS equation with the \(\delta\)-interaction on a star graph ⋮ Nodal statistics on quantum graphs ⋮ Quantum graphs which optimize the spectral gap ⋮ On the essential spectrum of quantum graphs ⋮ Nonlinear Schrödinger equations on periodic metric graphs ⋮ Ground states of nonlinear Schrödinger equation on star metric graphs ⋮ The spectrum of non-local discrete Schrödinger operators with a \(\delta\)-potential ⋮ Absolutely continuous spectrum for Laplacians on radial metric trees and periodicity ⋮ Localized asymptotic solutions of the wave equation with variable velocity on the simplest graphs ⋮ On the spectral properties of Dirac operators with electrostatic \(\delta\)-shell interactions ⋮ Relating zeta functions of discrete and quantum graphs ⋮ Quantum discord of states arising from graphs ⋮ Quantum graphs with vertices of a preferred orientation ⋮ Effective masses for Laplacians on periodic graphs ⋮ Nonlinear instability of half-solitons on star graphs ⋮ Functional model for extensions of symmetric operators and applications to scattering theory ⋮ Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators ⋮ Eigenfunctions of unbounded support for embedded eigenvalues of locally perturbed periodic graph operators ⋮ Compressed resolvents and reduction of spectral problems on star graphs ⋮ On the standing waves of the NLS-log equation with a point interaction on a star graph ⋮ A partial inverse problem for the Sturm-Liouville operator on the lasso-graph ⋮ NLS bifurcations on the bowtie combinatorial graph and the Dumbbell metric graph ⋮ NLS ground states on graphs ⋮ Scattering, spectrum and resonance states completeness for a quantum graph with Rashba Hamiltonian ⋮ Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential ⋮ The first eigenvalue of the \(p-\)Laplacian on quantum graphs ⋮ Trace formulas for Schrödinger operators on star graphs ⋮ Locality of the heat kernel on metric measure spaces ⋮ Eigenvalue inequalities and absence of threshold resonances for waveguide junctions ⋮ Sharp convergence rate of eigenvalues in a domain with a shrinking tube ⋮ Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model ⋮ Bi-Laplacians on graphs and networks ⋮ Resolvent expansion for the Schrödinger operator on a graph with infinite rays ⋮ On Agmon metrics and exponential localization for quantum graphs ⋮ Spectral theory of infinite quantum graphs ⋮ Dirac-Krein systems on star graphs ⋮ Existence of infinitely many stationary solutions of the \(L^{2}\)-subcritical and critical NLSE on compact metric graphs ⋮ Topological resonances on quantum graphs ⋮ Spectral properties of magnetic chain graphs ⋮ Concurrence and three-tangle of the graph ⋮ Standing waves for the NLS on the double-bridge graph and a rational-irrational dichotomy ⋮ The Cauchy problem for the wave equation on homogeneous trees ⋮ Negative energy ground states for the \(L^{2}\)-critical NLSE on metric graphs ⋮ Variational and stability properties of constant solutions to the NLS equation on compact metric graphs ⋮ Bifurcations of standing localized waves on periodic graphs ⋮ Standing waves of the quintic NLS equation on the tadpole graph ⋮ Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs ⋮ On the ground state for quantum graphs ⋮ Laplacians on periodic graphs with guides ⋮ Empirical spectral measures of quantum graphs in the Benjamini-Schramm limit ⋮ \(L^p-L^{p'}\) estimates for matrix Schrödinger equations ⋮ Instability of static solutions of the sine-Gordon equation on a \(\mathcal{Y}\)-junction graph with \(\delta\)-interaction ⋮ On the eigenvalues of quantum graph Laplacians with large complex \(\delta\) couplings ⋮ Effective operators for Robin eigenvalues in domains with corners ⋮ Partial inverse problems for the Sturm-Liouville operator on a star-shaped graph with different edge lengths ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem ⋮ Eigenspaces of symmetric graphs are not typically irreducible ⋮ Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs ⋮ Semiclassical eigenfunctions of the Schrödinger operator on a graph that are localized near a subgraph ⋮ Control and stabilization of \(2\times 2\) hyperbolic systems on graphs ⋮ The number of endpoints of a random walk on a semi-infinite metric path graph ⋮ Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization ⋮ Leaf peeling method for the wave equation on metric tree graphs ⋮ An inverse problem for quantum trees with observations at interior vertices ⋮ Lyndon word decompositions and pseudo orbits on \(q\)-nary graphs ⋮ Reducible Fermi surface for multi-layer quantum graphs including stacked graphene ⋮ Spectra of regular quantum trees: rogue eigenvalues and dependence on vertex condition ⋮ Spectral analysis on Barlow and Evans' projective limit fractals ⋮ Edge-localized states on quantum graphs in the limit of large mass ⋮ Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs ⋮ Variational properties and orbital stability of standing waves for NLS equation on a star graph ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ The semicircular law of free probability as noncommutative multivariable operator theory ⋮ On fully supported eigenfunctions of quantum graphs ⋮ A Glazman-Povzner-Wienholtz theorem on graphs ⋮ New relations between discrete and continuous transition operators on (metric) graphs ⋮ Resolvent of a Schrödinger operator on a model graph with small loops ⋮ Exotic eigenvalues of shrinking metric graphs ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ A time-dependent metric graph with a fourth-order operator on the edges ⋮ Inverse Problems for Discrete Heat Equations and Random Walks for a Class of Graphs ⋮ An Ambarzumian-type theorem on graphs with odd cycles ⋮ A geometric construction of isospectral magnetic graphs ⋮ On quantum star graphs with eigenparameter dependent vertex conditions ⋮ Initial boundary value problem for a time fractional wave equation on a metric graph ⋮ Spectrum of the Dirichlet Laplacian in a thin cubic lattice ⋮ NON-WEYL RESONANCE ASYMPTOTICS FOR QUANTUM GRAPH WITH THE DIRAC OPERATOR ON EDGES ⋮ Spectral decimation of piecewise centrosymmetric Jacobi operators on graphs ⋮ Inverse nodal problems for Sturm–Liouville operators on quantum star graphs ⋮ Interaction of in-plane waves with a structured penetrable line defect in an elastic lattice ⋮ The total variation flow in metric graphs ⋮ Classical and quantum wave dynamics on time-dependent geometric graph ⋮ Mean distance on metric graphs