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The essential spectrum of the Laplacian on rapidly branching tessellations. (English) Zbl 1285.05115

Summary: In this paper, we characterize absence of the essential spectrum of the Laplacian under a hyperbolicity assumption for general graphs. Moreover, we present a characterization for absence of the essential spectrum for planar tessellations in terms of curvature.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C65 Hypergraphs
47A10 Spectrum, resolvent
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