# Definition:Incident (Graph Theory)/Undirected Graph

< Definition:Incident (Graph Theory)(Redirected from Definition:Incident (Undirected Graph))

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## 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

- 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.**