On a theorem of Halin

Wilfried Imrich, Simon M. Smith

Research output: Contribution to journalArticleResearchpeer-review

Abstract

This note presents a new, elementary proof of a generalization of a theorem of Halin to graphs with unbounded degrees, which is then applied to show that every connected, countably infinite graph G, with ℵ0≤|Aut(G)|<2ℵ0 and subdegree-finite automorphism group, has a finite set F of vertices that is setwise stabilized only by the identity automorphism. A bound on the size of such sets, which are called distinguishing, is also provided. To put this theorem of Halin and its generalization into perspective, we also discuss several related non-elementary, independent results and their methods of proof.
Original languageEnglish
Pages (from-to)289-297
Number of pages9
JournalAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume87.2017
Issue numberOctober
DOIs
Publication statusPublished - 1 Oct 2017

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