Definition:Edge Set

Definition

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

The set $E$ of edges in $G$ is called the edge set.

It consists of (unordered) pairs of elements of the vertex set $V$.

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

Also see

• Definition:Vertex Set

• Results about edge 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): edge set