Definition:Incident (Graph Theory)/Undirected Graph

Definition
Let $G = \struct {V, E}$ be an undirected graph.

Let $u, v \in V$ be vertices of $G$.

Let $e = \set {u, v} \in E$ be an edge of $G$:


 * IncidentGraph.png

Then:
 * $u$ and $v$ are each incident with $e$
 * $e$ is incident with $u$ and incident with $v$.

Also known as
It is common to see incident to being used for incident with. For undirected graphs this is appropriate; for directed graphs the situation is more complicated.

Some sources use incident on.

Also see

 * Definition:Join (Graph Theory)