On infinite graphs with a primitive automorphism group (Q1331967)
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scientific article; zbMATH DE number 626310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On infinite graphs with a primitive automorphism group |
scientific article; zbMATH DE number 626310 |
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On infinite graphs with a primitive automorphism group (English)
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27 September 1994
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This article announces the following theorem: Let \(\Gamma\) be an infinite locally finite planar graph. Then \(\Gamma\) has a primitive automorphism group iff (a) \(\Gamma\) is 1-connected; (b) for some \(m\geq 2\) each vertex of \(\Gamma\) lies on exactly \(m\) lobes; and (c) the lobes of \(\Gamma\) are all isomorphic to \(K_ 4\) or are \(p\)-circuits, for some fixed prime \(p\). A complete proof will appear elsewhere.
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infinite locally finite planar graph
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automorphism group
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lobes
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