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Graphs and Combinatorics

, Volume 5, Issue 1, pp 333–338 | Cite as

A note on bounded automorphisms of infinite graphs

  • Chris D. Godsil
  • Wilfried Imrich
  • Norbert Seifter
  • Mark E. Watkins
  • Wolfgang Woess
Article

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.

Keywords

Normal Subgroup Automorphism Group Finite Order Polynomial Growth Finite Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Chris D. Godsil
    • 1
  • Wilfried Imrich
    • 2
  • Norbert Seifter
    • 2
  • Mark E. Watkins
    • 3
  • Wolfgang Woess
    • 2
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Institut für Mathematik und Angewandte Geometrie, MontanuniversitätLeobenAustria
  3. 3.Department of MathematicsSyracuse UniversitySyracuseUSA

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