Definition:Vertex Set

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Let $G = \struct {V, E}$ be a graph.

The set $V$ of vertices in $G$ is called the vertex set.

It is often convenient to refer to the vertex set for a given graph $G$ as $\map V G$, especially if there is at any one time more than one graph under consideration.

Also defined as

Some sources further specify that the vertex set cannot be empty.

That is, that a graph must have at least one vertex.

Hence such sources do not raise the concept of a null graph.

Also see