Rooted tree

This category corresponds roughly to MSC {{{id}}} {{{title}}}; see {{{id}}} at MathSciNet and {{{id}}} at zbMATH.

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

An example of rooted tree

Rooted trees play a central rôle in Butcher series and the algebraic notion of pre-Lie algebra.