Definition:Digraph/Arc
< Definition:Digraph(Redirected from Definition:Arc of Digraph)
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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 $v$.
Also see
- Results about arcs of digraphs can be found here.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.5$: Directed Graphs as Mathematical Models
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): arc: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): arc: 2.
- 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): arc: 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): arc (of a digraph)