Name: The Spectrum of an Infinite Graph
Creator: Hajime Urakawa
Keywords: Fractals, spectrum of the discrete Laplacian, Graphs and linear algebra (matrices, eigenvalues, etc.), 0101 mathematics, 16. Peace & justice, Discrete potential theory, 01 natural sciences, infinite graph

The spectrum of an infinite graph

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 2000 English Publisher:Canadian Mathematical SocietyJournal:Canadian Journal of Mathematics, volume 52, pages 1,057-1,084 (issn: 0008-414X, eissn: 1496-4279,

Authors: Hajime Urakawa;

doi: 10.4153/cjm-2000-044-2

The Spectrum of an Infinite Graph

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Abstract

AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.

Related Organizations

Tohoku University
Japan

Keywords

Fractals, spectrum of the discrete Laplacian, Graphs and linear algebra (matrices, eigenvalues, etc.), Discrete potential theory, infinite graph

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