Singleton Graph is Complete

Theorem

The singleton graph $N_1$ is complete.

Proof

Recall the definition of $N_1$:

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

Recall the definition of complete graph:

Let $G = \struct {V, E}$ be a simple graph such that every vertex is adjacent to every other vertex.

Then $G$ is called complete.

The complete graph of order $p$ is denoted $K_p$.

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

$\blacksquare$

Sources

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