### 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 K_{4} or all are circuits of length p for some odd prime p.

Original language | English (US) |
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Pages (from-to) | 87-104 |

Number of pages | 18 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - 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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## Cite this

Watkins, M. E., & Graver, J. E. (2004). A characterization of infinite planar primitive graphs.

*Journal of Combinatorial Theory. Series B*,*91*(1), 87-104. https://doi.org/10.1016/j.jctb.2003.10.005