Difference between revisions of "Rooted tree"
From Encyclopedia of Mathematics
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A [[tree]] with a distinguished vertex, the ''root''. A rooted tree has a natural [[Graph, oriented|orientation]] in which all paths are directed away from the root: such an oriented tree is an ''[[arborescence]]''. | A [[tree]] with a distinguished vertex, the ''root''. A rooted tree has a natural [[Graph, oriented|orientation]] in which all paths are directed away from the root: such an oriented tree is an ''[[arborescence]]''. | ||
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| + | A ''rooted plane tree'' is one with a prescribed cyclic order of the edges incident with each vertex. | ||
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| + | [[File:Rooted tree 230000.svg|center|200px|An example of rooted tree]] | ||
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| + | Rooted trees play a central rôle in [[Butcher series]] and the algebraic notion of [[pre-Lie algebra]]. | ||
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| + | [[Category:Graph theory]] | ||
Latest revision as of 08:23, 12 November 2023
2020 Mathematics Subject Classification: Primary: 05C05 [MSN][ZBL]
A tree with a distinguished vertex, the root. A rooted tree has a natural orientation in which all paths are directed away from the root: such an oriented tree is an arborescence.
A rooted plane tree is one with a prescribed cyclic order of the edges incident with each vertex.
Rooted trees play a central rôle in Butcher series and the algebraic notion of pre-Lie algebra.
How to Cite This Entry:
Rooted tree. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rooted_tree&oldid=38553
Rooted tree. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rooted_tree&oldid=38553