Definition:Edgeless Graph

Definition
An edgeless graph is a graph with no edges.

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

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

The edgeless graph of order $n$ is denoted $N_n$.

By definition, all vertices of an edgeless graph are isolated.

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.