Definition:Vertex Set

Definition

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

• Definition:Edge Set

• Results about vertex sets can be found here.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs
• 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $2$. Graphs: Graphs
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): vertex set