Definition:Rooted Tree/Parent Node

Definition
Let $T$ be a rooted tree whose root is $r_T$.

Let $t$ be a node of $T$.

From Path in Tree is Unique, there is only one path from $t$ to $r_T$.

Let $\pi: T \setminus \set {r_T} \to T$ be the mapping defined by:


 * $\map \pi t := \text {the node adjacent to $t$ on the path to $r_T$}$

Then $\map \pi t$ is known as the parent node of $t$.

The mapping $\pi$ is called the parent mapping.