A characterization of infinite planar primitive graphs

Mark E. Watkins, Jack E Graver

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Graph Connectivity
Networks (circuits)
Graph in graph theory
Vertex of a graph
Planar graph
Automorphism Group
Isomorphic
Odd
If and only if
Integer

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

A characterization of infinite planar primitive graphs. / Watkins, Mark E.; Graver, Jack E.

In: Journal of Combinatorial Theory, Series B, Vol. 91, No. 1, 05.2004, p. 87-104.

Research output: Contribution to journalArticle

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