A characterization of infinite planar primitive graphs

Mark E. Watkins, Jack E. Graver

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

It is shown that the automorphism group of an infinite, locally finite, planar graph acts primitively on its vertex set if and only if the graph has connectivity 1 and, for some integer m≥2, every vertex is incident with exactly m lobes, all of which are finite. Specifically, either all of the lobes are isomorphic to K4 or all are circuits of length p for some odd prime p.

Original languageEnglish (US)
Pages (from-to)87-104
Number of pages18
JournalJournal of Combinatorial Theory. Series B
Volume91
Issue number1
DOIs
StatePublished - May 2004

Keywords

  • Edge-transitive
  • Infinite planar map
  • Primitive permutation group

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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