Definition:Edgeless Graph

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.

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 Edgeless 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

 * Graph is 0-Regular iff Edgeless


 * Edgeless Graph is Bipartite


 * Edgeless Graph of Order n has n Components


 * Complete Graph of Order 1 is Edgeless


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


 * $N_1$ is a tree while for all $n > 1$, $N_n$ is a forest.