A note on bounded automorphisms of infinite graphs

C. Godsil; Wilfried Imrich; Norbert Seifter; Mark Watkins; Wolfgang Woess

doi:10.1007/BF01788688

A note on bounded automorphisms of infinite graphs

C. Godsil
, Wilfried Imrich
, Norbert Seifter
, Mark Watkins
, Wolfgang Woess

Chair of Applied Mathematics (170)

University of Waterloo
Syracuse University

Research output: Contribution to journal › Article › Research › peer-review

20 Citations (Scopus)

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.

Original language	Undefined/Unknown
Pages (from-to)	333-338
Number of pages	6
Journal	Graphs and combinatorics
Volume	5.1989
Issue number	December
DOIs	https://doi.org/10.1007/BF01788688
Publication status	Published - 1989

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title = "A note on bounded automorphisms of infinite graphs",

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.",

author = "C. Godsil and Wilfried Imrich and Norbert Seifter and Mark Watkins and Wolfgang Woess",

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AU - Godsil, C.

AU - Imrich, Wilfried

AU - Seifter, Norbert

AU - Watkins, Mark

AU - Woess, Wolfgang

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

UR - https://doi.org/10.1007/BF01788688

U2 - 10.1007/BF01788688

DO - 10.1007/BF01788688

M3 - Article

VL - 5.1989

SP - 333

EP - 338

JO - Graphs and combinatorics

JF - Graphs and combinatorics

IS - December

ER -

A note on bounded automorphisms of infinite graphs

Abstract

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