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.
How to Cite This Entry:
Rooted tree. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rooted_tree&oldid=54371
Rooted tree. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rooted_tree&oldid=54371