Curvature, geometry and spectral properties of planar graphs
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Publication:644818
DOI10.1007/s00454-011-9333-0zbMath1228.05129arXiv1101.2970OpenAlexW1976591270WikidataQ126116311 ScholiaQ126116311MaRDI QIDQ644818
Publication date: 7 November 2011
Published in: Discrete \& Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1101.2970
cut locusexponential growthspectrum of graphsdiscrete curvatureCheeger's constanthyperbolic propertiesunique continuation of eigenfunctions
Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)
Related Items (21)
Total curvature of planar graphs with nonnegative combinatorial curvature ⋮ Strong isoperimetric inequalities and combinatorial curvatures on multiply connected planar graphs ⋮ Curvature notions on graphs ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ Applications of Signatures Curves to Characterize Melanomas and Moles ⋮ The set of vertices with positive curvature in a planar graph with nonnegative curvature ⋮ Strong Isoperimetric Inequality for Tessellating Quantum Graphs ⋮ Characterising planar Cayley graphs and Cayley complexes in terms of group presentations ⋮ Every graph is a cut locus ⋮ Sectional curvature of polygonal complexes with planar substructures ⋮ Eigenfunctions and the integrated density of states on Archimedean tilings ⋮ An overview of curvature bounds and spectral theory of planar tessellations ⋮ Cubic graphs and the golden mean ⋮ A curvature notion for planar graphs stable under planar duality ⋮ Eigenvalue asymptotics for Schrödinger operators on sparse graphs ⋮ Duality properties of strong isoperimetric inequalities on a planar graph and combinatorial curvatures ⋮ A note on the surjectivity of operators on vector bundles over discrete spaces ⋮ Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II ⋮ Hyperbolic polyhedral surfaces with regular faces ⋮ On the largest planar graphs with everywhere positive combinatorial curvature ⋮ Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem
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