\begin{definition}[Definition:Rooted Tree/Parent Node]
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 $\pi: T \setminus \left\{{r_T}\right\} \to T$ be the mapping defined by:
:$\pi \left({t}\right) := \text{the node adjacent to $t$ on the path to $r_T$}$
Then $\pi \left({t}\right)$ is known as the '''parent node''' of $t$.
The mapping $\pi$ is called the '''parent mapping'''.
\end{definition}