Definition:Incident (Graph Theory)/Planar Graph

Definition

Let $G = \struct {V, E}$ 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 $BCEF$ is incident to:

the edges $BC, CE, EF, FB$

the vertices $B, C, E, F$.

Also see

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