# Definition:Rooted Tree/Parent Node

< Definition:Rooted Tree(Redirected from Definition:Parent Node)

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## 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**.

## Also known as

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.

## Examples

### Arbitrary Example

Consider the rooted tree below:

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

## Also see

- Results about
**parent nodes**can be found**here**.

## Sources

- 1979: John E. Hopcroft and Jeffrey D. Ullman:
*Introduction to Automata Theory, Languages, and Computation*... (previous) ... (next): Chapter $1$: Preliminaries: $1.2$ Graphs and Trees: Trees - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.7$: Tableaus