# 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.