Editing Tree (graph theory) (section)

=== {{anchor|Plane tree}} Ordered tree===
An ''ordered tree'' (alternatively, ''plane tree'' or ''positional tree''<ref>{{cite book |last1=Cormen |first1=Thomas H. |last2=Leiserson |first2=Charles E. |last3=Rivest |first3=Ronald L. |last4=Stein |first4=Clifford |title=Introduction to Algorithms |date=2022 |publisher=MIT Press |location=Section B.5.3, ''Binary and positional trees'' |isbn=9780262046305 |page=1174 |edition=4th |url=https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/ |access-date=20 July 2023 |archive-date=16 July 2023 |archive-url=https://web.archive.org/web/20230716082232/https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/ |url-status=live }}</ref>) is a rooted tree in which an ordering is specified for the children of each vertex.{{sfn|Bender|Williamson|2010|p=173}}<ref>{{citation|title=Enumerative Combinatorics, Vol. I|volume=49|series=Cambridge Studies in Advanced Mathematics|first=Richard P.|last=Stanley|author-link=Richard P. Stanley|publisher=Cambridge University Press|year=2012|isbn=9781107015425|page=573|url=https://books.google.com/books?id=0wmJntp8IBQC&pg=PA573}}</ref> This is called a "plane tree" because an ordering of the children is equivalent to an embedding of the tree in the plane, with the root at the top and the children of each vertex lower than that vertex. Given an embedding of a rooted tree in the plane, if one fixes a direction of children, say left to right, then an embedding gives an ordering of the children. Conversely, given an ordered tree, and conventionally drawing the root at the top, then the child vertices in an ordered tree can be drawn left-to-right, yielding an essentially unique planar embedding.