Page "Tree (graph theory)" Paragraph 22

An or plane tree is a rooted tree for which an ordering is specified for the children of each vertex.

This is called a " plane tree " because an ordering of the children is equivalent to an embedding of the tree in the plane ( up to homotopy through embeddings or ambient isotopy ).

Given an embedding of a rooted tree in the plane, if one fixes a direction of children ( starting from root, then first child, second child, etc.

), say counterclockwise, then an embedding gives an ordering of the children.

Conversely, given an ordered tree, and conventionally draw the root at the top, then the child nodes in an ordered tree can be drawn left-to-right, yielding an essentially unique planar embedding ( up to embedded homotopy, i. e., moving the edges and nodes without crossing ).