# Definition:Tree (Graph Theory)

## Definition

### Definition 1

A tree is a simple connected graph with no circuits.

### Definition 2

A tree is a simple connected graph with no cycles.

## Node

The vertices of a tree are called its nodes.

## Leaf Node

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.

## Finite or Infinite

### Finite Tree

A tree is finite if and only if it contains a finite number of nodes.

### Infinite Tree

A tree is infinite if it contains a (countably) infinite number of nodes.

## Also defined as

In some contexts, the term tree is used to mean rooted tree.

## Also see

• Results about trees can be found here.