A characterization of infinite planar primitive graphs

Mark E. Watkins; Jack E. Graver

doi:10.1016/j.jctb.2003.10.005

A characterization of infinite planar primitive graphs

Mark E. Watkins, Jack E. Graver

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	87-104
Number of pages	18
Journal	Journal of Combinatorial Theory. Series B
Volume	91
Issue number	1
DOIs	https://doi.org/10.1016/j.jctb.2003.10.005
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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10.1016/j.jctb.2003.10.005

Cite this

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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.",

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AU - Graver, Jack E.

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AB - 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.

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KW - Infinite planar map

KW - Primitive permutation group

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JO - Journal of Combinatorial Theory. Series B

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A characterization of infinite planar primitive graphs

Abstract

Keywords

ASJC Scopus subject areas

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