Graph Laplacians and topology

DOI10.1007/s11512-007-0059-4zbMath1205.47044OpenAlexW2059594753MaRDI QIDQ942041

Pavel Kurasov

Publication date: 3 September 2008

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11512-007-0059-4

zbMATH Keywords

Laplace operatorspectral propertiesmetric graph

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Scattering theory of linear operators (47A40)

Related Items (22)

Isospectrality for graph Laplacians under the change of coupling at graph vertices ⋮ Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph ⋮ ISOSPECTRALITY FOR GRAPH LAPLACIANS UNDER THE CHANGE OF COUPLING AT GRAPH VERTICES: NECESSARY AND SUFFICIENT CONDITIONS ⋮ Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples ⋮ On inverse topology problem for Laplace operators on graphs ⋮ The nodal count {0,1,2,3,…} implies the graph is a tree ⋮ Imaging geometric graphs using internal measurements ⋮ Rayleigh estimates for differential operators on graphs ⋮ Gelfand's inverse problem for the graph Laplacian ⋮ Path Laplacian matrices: introduction and application to the analysis of consensus in networks ⋮ Inverse Problems for Discrete Heat Equations and Random Walks for a Class of Graphs ⋮ 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 ⋮ Resolvent expansions on hybrid manifolds ⋮ \(n\)-Laplacians on metric graphs and almost periodic functions. I ⋮ Gluing graphs and the spectral gap: a Titchmarsh–Weyl matrix-valued function approach ⋮ Stable polynomials and crystalline measures ⋮ Inverse problems for Aharonov–Bohm rings ⋮ Schrödinger operators on graphs and geometry I: Essentially bounded potentials ⋮ Schrödinger operators on graphs: Symmetrization and Eulerian cycles ⋮ Schrödinger operators on graphs and geometry. II: Spectral estimates for \(L_1\)-potentials and an Ambartsumian theorem ⋮ Asymptotically isospectral quantum graphs and generalised trigonometric polynomials

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