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A note on bounded automorphisms of infinite graphs

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Abstract

LetX be a connected locally finite graph with vertex-transitive automorphism group. IfX has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup ofAUT(X) and the action ofAUT(X) onV(X) is imprimitive ifX is not finite. IfX has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic.

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Authors and Affiliations

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

    Chris D. Godsil

  2. Institut für Mathematik und Angewandte Geometrie, Montanuniversität, A-8700, Leoben, Austria

    Wilfried Imrich, Norbert Seifter & Wolfgang Woess

  3. Department of Mathematics, Syracuse University, 13244-1150, Syracuse, NY, USA

    Mark E. Watkins

Authors
  1. Chris D. Godsil
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  2. Wilfried Imrich
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  3. Norbert Seifter
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  4. Mark E. Watkins
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  5. Wolfgang Woess
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Godsil, C.D., Imrich, W., Seifter, N. et al. A note on bounded automorphisms of infinite graphs. Graphs and Combinatorics 5, 333–338 (1989). https://doi.org/10.1007/BF01788688

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  • DOI: https://doi.org/10.1007/BF01788688

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