Singleton Graph is Regular

Theorem

The singleton graph $N_1$ is regular of degree $0$.

Proof

Recall the definition of $N_1$:

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

Recall the definition of regular graph:

Let $G = \struct {V, E}$ be an simple graph whose vertices all have the same degree $r$.

Then $G$ is called regular of degree $r$, or $r$-regular.

As $N_1$ has only one vertex, this follows vacuously.

$\blacksquare$