Rooted tree

Definition

A rooted tree is a pair $(T, r)$ of a tree $T$ and a vertex $r$ of $T$, the root.

Let $v \neq r$ be a vertex, and let $u$ be the neighbour of $v$ on the unique path from $v$ to $r$. Then $u$ is the parent of $v$, and $v$ is a child of $u$. The depth of $v$ is the distance from $r$ to $v$.

Remarks

The root has no parent, and every other vertex has exactly one parent. A vertex with no child is a leaf of the rooted tree. With this convention the root can be a leaf only when the tree has one vertex. An ordered rooted tree also fixes an order of the children of each vertex. A binary tree is a related recursive structure.

Explanations

L1 human

A rooted tree is a tree in which one vertex is chosen as the top. Then each edge has a direction: from a parent toward its child, away from the root.