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Graphs with polynomial growth are covering graphs

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Abstract

LetX be a connected locally finite transitive graph with polynomial growth. We show that there exist infinitely many finite graphsY 1,Y 2,... such thatX is a covering graph of each of these graphs and everyY k ,k≥2, is covering graph of the graphsY 1,...,Y k-1 . IfX is in additions-transitive for somes≥2 the graphsY i can be assumed to be at leasts-transitive.

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Author notes

  1. N. Seifter

    Present address: f. Mathematik, Montanuniversitaet Leoben, A-8700, Leoben, Austria

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    C. D. Godsil & N. Seifter

Authors
  1. C. D. Godsil
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  2. N. Seifter
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Additional information

Work of both authors was in part supported by NSERC grant A5367.

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Godsil, C.D., Seifter, N. Graphs with polynomial growth are covering graphs. Graphs and Combinatorics 8, 233–241 (1992). https://doi.org/10.1007/BF02349960

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  • DOI: https://doi.org/10.1007/BF02349960

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