(definition)
Definition: The dual of a planar graph, G, is a graph with a vertex for each region in G and an edge between vertices for each pair of adjacent regions. The new edge crosses the edge in G which is the boundary between the adjacent regions.
Generalization (I am a kind of ...)
planar graph.
Note:
The dual of a planar graph is also planar. The original graph is the dual of the dual. That is, they are duals of each other.
In the accompanying figure, the black circles and solid lines are one planar graph. The white squares and dotted lines are another planar graph. Each is the dual of the other.
Author: PEB
Herman Servatius' Self-dual maps, that is, planar graphs that are duals of themselves.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 19 March 2007.
HTML page formatted Mon Mar 19 11:55:26 2007.
Cite this as:
Paul E. Black, "dual", in
Dictionary of Algorithms and Data
Structures [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 19 March 2007. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/dual.html
