# Definition:Edgeless Graph

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## Definition

An **edgeless graph** is a graph with no edges.

That is, an **edgeless graph** is a graph of size zero.

Equivalently, an **edgeless graph** is a graph whose vertices are all isolated.

The **edgeless graph** of order $n$ is denoted $N_n$ and can be referred to as the **$n$-edgeless graph**.

## Examples

The edgeless graphs of order $1$ to $5$ are illustrated below:

## Also known as

This is sometimes called an **empty graph**.

Thus the term **$n$-empty graph** can often be seen for $N_n$.

The symbol $\overline K_n$ is frequently used to denote the **$n$-edgeless graph**, which follows from Complement of Complete Graph is Edgeless Graph.

The term **null graph** can also be found, but this can be confused with the graph with no vertices.

## Also see

- Results about
**edgeless graphs**can be found here.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs

- Weisstein, Eric W. "Empty Graph." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/EmptyGraph.html