# Definition:Rooted Tree/Parent Node

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## Definition

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**.

## Also known as

The node $\pi \left({t}\right)$ is often simply called the **parent** of $t$.

The mapping $\pi$ is also called the **parent function**.

## Sources

- 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*... (previous) ... (next): $\S 1.7$: Tableaus