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 $G$:

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 digraph the situation is more complicated.

Some sources use incident on.

Some sources use the term adjacent for incident.

Also see

• Definition:Join (Graph Theory)

• Results about incidence in the context of graph theory can be found here.

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): adjacent: 3.