Some relations between analytic and geometric properties of infinite graphs

DOI10.1016/0012-365X(91)90337-2zbMath0801.05051MaRDI QIDQ1191921

Bojan Mohar

Publication date: 27 September 1992

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

growthinvariantsamenabilityspectraisoperimetric numberKazhdan property

Mathematics Subject Classification ID

Applications of graph theory (05C90) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Structural characterization of families of graphs (05C75) Graph theory (05C99)

Related Items (17)

Spectral estimates for infinite quantum graphs ⋮ The growth rate and balance of homogeneous tilings in the hyperbolic plane ⋮ Spectral radius of finite and infinite planar graphs and of graphs of bounded genus ⋮ Invariants for Laplacians on periodic graphs ⋮ A survey of graph laplacians ⋮ Percolation on infinite graphs and isoperimetric inequalities ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ Self-Avoiding Walks and Connective Constants ⋮ On the Laplacian spectrum of an infinite graph ⋮ Schrödinger operators on periodic discrete graphs ⋮ Laplacians on periodic graphs with guides ⋮ Cubic graphs and the golden mean ⋮ Eigenvalue asymptotics for Schrödinger operators on sparse graphs ⋮ Essential spectrum and Weyl asymptotics for discrete Laplacians ⋮ Branching Random Walks on $Z^d$ with Periodic Branching Sources ⋮ Geometry and spectrum of rapidly branching graphs ⋮ Norms, kernels and eigenvalues of some infinite graphs

Cites Work

• Amenability, unimodularity, and the spectral radius of random walks on infinite graphs
• Random walks on graphs with a strong isoperimetric property
• Isoperimetric inequalities, growth, and the spectrum of graphs
• The fundamental group and the spectrum of the Laplacian
• Connection of the dual space of a group with the structure of its closed subgroups
• On groups with full Banach mean value
• A Survey on Spectra of infinite Graphs
• Amenability for discrete convolution semigroup algebras.
• Compact Perturbations, Normal Eigenvalues and a Problem of Salinas
• Invariant Measures and Growth Conditions
• A Finitely Presented Group Whose 3-Dimensional Integral Homology is not Finitely Generated
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