Fixed elements of infinite trees (Q1331970)
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scientific article; zbMATH DE number 626313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed elements of infinite trees |
scientific article; zbMATH DE number 626313 |
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Fixed elements of infinite trees (English)
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29 August 1994
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The automorphism group of a rayless tree fixes a vertex or a set of two adjacent vertices. The authors provide a short proof of this fact. For an alternate approach see [\textit{R. Schmidt}, Ein Ordnungsbegriff für Graphen ohne unendliche Wege mit einer Anwendung auf \(n\)-fach zusammenhängende Graphen, Arch. Math. 40, 283-288 (1983; Zbl 0526.05058)]. The same conclusion is shown to hold for trees which contain at least three ends of maximum order and no subgraph homeomorphic to the dyadic tree.
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infinite trees
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automorphism group
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rayless tree
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ends
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dyadic tree
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