Complete Graph of Order 1 is Edgeless

Theorem

The complete graph $K_1$ of order $1$ is the edgeless graph $N_1$.

Proof

By definition, $K_1$ has $1$ vertex.

From Complete Graph is Regular, $K_1$ is $0$-regular.

Hence the result from Graph is 0-Regular iff Edgeless.

$\blacksquare$