Rooted tree

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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.

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