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