Definition:Rooted Tree/Child Node

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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:

$\left\{{s \in T: \pi \left({s}\right) = t}\right\}$

where $\pi \left({s}\right)$ 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:

$\pi \left({\pi \left({s}\right)}\right) = t$

Also known as

Child nodes are often referred to as just children.