# Definition:Tree (Graph Theory)/Leaf Node

Jump to navigation
Jump to search

## Definition

Let $v$ be a node of a tree $T$.

Then $v$ is a **leaf node** of a $T$ if and only if $v$ is of degree $1$.

If $T$ is a rooted tree, this is equivalent to saying that $v$ has no child nodes.

## Also known as

A **leaf node** is also known as just a **leaf**.

In the context of rooted trees, a **leaf node** is often referred to as a **terminal node**.

In the context of more general graphs which are not trees, a degree $1$ vertex is known as a **pendant vertex** or an **end vertex**.

## Examples

### Arbitrary Example

Consider the rooted tree below:

The **leaf nodes** are $2$, $4$, $6$, $8$ and $9$.

## Also see

- Results about
**leaf 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