# Definition:Rooted Tree/Child Node

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## Definition

Let $T$ be a rooted tree with root $r_T$.

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

The **child nodes** of $t$ are the elements of the set:

- $\set {s \in T: \map \pi s = t}$

where $\map \pi s$ denotes the parent mapping of $s$.

That is, the **children** of $t$ are all the nodes of $T$ of which $t$ is the parent.

### Grandchild Node

A child of a child node of a node $t$ can be referred to as a **grandchild node** of $t$.

In terms of the parent mapping $\pi$ of $T$, a **grandchild node** of $t$ is a node $s$ such that:

- $\map \pi {\map \pi s} = t$

## Also known as

**Child nodes** are often referred to as just **children**.

Some sources use the term **son** instead of **child**, but this is considered old-fashioned nowadays.

## Examples

### Arbitrary Example

Consider the rooted tree below:

The **child nodes** of node $5$ are nodes $7$ and $8$.

## Also see

- Results about
**child 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