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 $N_n$.

Also known as
This is sometimes called an empty graph or null graph, but the latter term can be confused with the graph with no vertices.

Basic Properties

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


 * The edgeless graph $N_n$ is (vacuously) bipartite 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 $K_n$.


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