Category:Definitions/Faces of Graphs
This category contains definitions related to Faces of Graphs.
Related results can be found in Category:Faces of Graphs.
The faces of a planar graph are the areas which are surrounded by edges.
In the above, the faces are $BCEF$, $ABF$, $CFG$, $AFG$ and $ABCDCEG$.
Incident
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:
Adjacent
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.
Pages in category "Definitions/Faces of Graphs"
The following 4 pages are in this category, out of 4 total.