# 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 $N_n$.

## 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 **$n$-empty graph**, which follows from Empty Graph is Complement of Complete Graph.

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

## Also see

- The edgeless graph $N_n$ is $0$-regular for all $n$.

- The edgeless graph $N_n$ has $n$ components for all $n$.

- $N_1$ is the complete graph $K_1$ and also the path graph $P_1$.

- The complement of $N_n$ is the complete graph $K_n$.

## Sources

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

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