# Rooted tree

From Encyclopedia of Mathematics

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.

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Rooted tree.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Rooted_tree&oldid=54371