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Approximating graphs with polynomialgrowth

Published online by Cambridge University Press:  07 August 2001

Norbert Seifter  and
Wolfgang Woess
Norbert Seifter
Affiliation:
Institut für Mathematik und Angewandte Geometrie, Montanuniversität Leoben, A-8700 Leoben, Austria
Wolfgang Woess
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá di Milano “Bicocca”, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy Present address: Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
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Abstract

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Let X be an infinite, locally finite, almost transitive graph with polynomial growth. We show that such a graph X is the inverse limit of an infinite sequence of finite graphs satisfying growth conditions which are closely related to growth properties of the infinite graph X.

1991 Mathematics Subject Classification. Primary 05C25, Secondary 20F8.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 1 - 8
Copyright
2000 Glasgow Mathematical Journal Trust