Graph Laplacians and topology
type: Item
instance of: scholarly article
title: Graph Laplacians and topology
zbMATH Open document ID: 1205.47044
author: Pavel Kurasov
published in: Arkiv för Matematik
publication date: 2008-09-03T00:00:00Z
review text: Sturm-Liouville operators on metric graphs with zero potential are studied. It is shown that the spectrum and scattering data determine the length of the compact part of the graph, the number of connected components and the Euler characteristic.
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47A40
zbMATH DE Number: 5319834
zbMATH Keywords: metric graph
zbMATH Keywords: Laplace operator
zbMATH Keywords: spectral properties
reviewed by: V. A. Yurko
MaRDI profile type: Publication
full work available at URL: s11512-007-0059-4
OpenAlex ID: W2059594753
cites work: Boundary spectral inverse problem on a class of graphs (trees) by the BC method
cites work: On the boundary controllability of dynamical system described by the wave equation on a class of graphs (on trees)
cites work: Can one hear the shape of a network?
cites work: Symmetries of quantum graphs and the inverse scattering problem
cites work: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
cites work: A Borg–Levinson theorem for trees
cites work: Inverse eigenvalue problems on directed graphs
cites work: Free quantum motion on a branching graph
cites work: Genericity of simple eigenvalues for a metric graph
cites work: Scattering problems on noncompact graphs
cites work: Can one hear the shape of a graph?
cites work: Kirchhoff's rule for quantum wires
cites work: Kirchhoff's rule for quantum wires. II: The inverse problem with possible applications to quantum computers
cites work: Periodic orbit theory and spectral statistics for quantum graphs
cites work: Inverse spectral problem for quantum graphs
cites work: On the inverse scattering problem on branching graphs
cites work: Discrete Schrödinger operators and topology
cites work: Inverse Spectral Problem for Quantum Graphs with Rationally Dependent Edges
cites work: SCHRÖDINGER OPERATORS ON HOMOGENEOUS METRIC TREES: SPECTRUM IN GAPS
cites work: Q4454220
cites work: Inverse spectral problems for Sturm–Liouville operators on graphs
DOI: 10.1007/S11512-007-0059-4
description: scientific article; zbMATH DE number 5319834