Definition:Singleton Graph

Definition

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

Also known as

The singleton graph can also be referred to as:

• The $1$-edgeless graph $N_1$

• The $1$-complete graph $K_1$

• The $1$-path graph $P_1$

Also see

• Singleton Graph is Unique, justifying our wording of this as the singleton graph

• Singleton Graph is Edgeless

• Singleton Graph is Complete

• Singleton Graph is Regular

• Singleton Graph is Path Graph

• Singleton Graph is Cycle Graph

• Singleton Graph is Complete Bipartite Graph

• Singleton Graph is Tree

• Results about the singleton graph can be found here.

Sources

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