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.

The node $\map \pi t$ is often simply called the parent of $t$.

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

Some sources use the word father for parent, but this is considered old-fashioned nowadays.

Consider the rooted tree below:

The parent node of node $5$ is node $3$.