A characterization of infinite planar primitive graphs

Mark E. Watkins, Jack E. Graver

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number1
StatePublished - May 2004


  • 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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