Edgeless Graph of Order 1 is Tree

Theorem

Let $N_1$ denote the edgeless graph with $1$ vertex.

Then $N_1$ is a tree.

Proof

By definition, a tree is a simple connected graph with no circuits.

$N_1$ is trivially connected graph.

As $N_1$ is edgeless, it has no edges.

But a circuit is a closed trail with at least one edge.

Hence the result.

$\blacksquare$