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The Spectrum of an Infinite Graph

Published online by Cambridge University Press:  20 November 2018

Hajime Urakawa
Hajime Urakawa*
Affiliation:
Mathematics Labratories, Graduate School of Information Sciences, Tohoku University, Katahira 2-1-1, Sendai 980-8577, JAPAN email: urakawa@math.is.tohoku.ac.jp
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Abstract

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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

05C5058G25infinite graphdiscrete Laplacianspectrumessential spectrum
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 5 , 01 October 2000 , pp. 1057 - 1084
Copyright
Copyright © Canadian Mathematical Society 2000

References

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