# Definition:Incident (Graph Theory)

## Undirected Graph

Let $G = \left({V, E}\right)$ be an undirected graph.

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

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

$u$ and $v$ are each incident with $e$
$e$ is incident with $u$ and incident with $v$.

## Digraph

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

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

Let $e = \tuple {u, v}$ be an arc that is directed from $u$ to $v$: Then the following definitions are used:

### Incident From

$e$ is incident from $u$
$v$ is incident from $e$.

### Incident To

$e$ is incident to $v$
$u$ is incident to $e$.

## Planar Graph Let $G = \left({V, E}\right)$ be a planar graph:

Then a face of $G$ is incident to an edge $e$ of $G$ if $e$ is one of those which surrounds the face.

Similarly, a face of $G$ is incident to a vertex $v$ of $G$ if $v$ is at the end of one of those incident edges.

In the above graph, for example, the face $ABHC$ is incident to:

the edges $AB, BH, HC, CA$
the vertices $A, B, H, C$.