Singleton Graph is Edgeless

Theorem

The singleton graph $N_1$ is edgeless.

Proof

Recall the definition of $N_1$:

The singleton graph $N_1$ is the simple graph with one vertex:

As $N_1$ is simple, the only edges are between distinct vertices.

As $N_1$ has only one vertex, $N_1$ can have no edges.

$\blacksquare$

Sources

• Weisstein, Eric W. "Singleton Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SingletonGraph.html