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The Spectrum of an Infinite Graph

  Published:2000-10-01
 Printed: Oct 2000
  • Hajime Urakawa
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Abstract

In 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.
Keywords: infinite graph, discrete Laplacian, spectrum, essential spectrum infinite graph, discrete Laplacian, spectrum, essential spectrum
MSC Classifications: 05C50, 58G25 show english descriptions Graphs and linear algebra (matrices, eigenvalues, etc.)
unknown classification 58G25
05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.)
58G25 - unknown classification 58G25
 

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