Definition:Graph (Graph Theory)/Edge

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This page is about edge of graph. For other uses, see edge.

Definition

ExampleOfGraph.png


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

The edges are the elements of $E$.


In the above, the edges are $AB, AE, BE, CD, CE, CF, DE, DF, FG$.


Join

Let $u$ and $v$ be vertices of $G$.

Let $e = u v$ be an edge of $G$.


Then $e$ joins the vertices $u$ and $v$.


Notation

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

If $G$ is an undirected graph, an edge $u v$ can equivalently be denoted $v u$.


Endvertex

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

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


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


Also see

When $G$ is a digraph, the edges are usually called arcs.

  • Results about edges of graphs can be found here.


Sources

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