Definition:Adjacent (Graph Theory)/Faces

This page is about Adjacent Faces of Graph. For other uses, see Adjacent Faces.

Definition

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

Two faces of $G$ are adjacent if and only if they are both incident to the same edge (or edges).

In the above diagram, $BCEF$ and $ABF$ are adjacent, but $BCEF$ and $AFG$ are not adjacent.

Note that faces which are both incident to the same vertex are not considered adjacent unless they are also both incident to the same edge.

Also known as

Adjacent elements of a graph can also be described as neighboring (British English spelling: neighbouring).