Definition:Directed Graph/Arc

Definition

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

The arcs are the elements of $E$.

Informally, an arc is a line that joins one vertex to another.

If $e \in E$ is an arc joining the vertex $u$ to the vertex $v$, it is denoted $u v$.

Endvertex

Let $D = \struct {V, E}$ be a digraph.

Let $e = u v$ be an arc of $D$, that is, $e \in E$.

The endvertices of $e$ are the vertices $u$ and $v$.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.5$: Directed Graphs as Mathematical Models
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: arc (of a digraph)