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Difference between revisions of "Rooted tree"

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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.

An example of rooted tree

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