(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

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Entry modified 27 December 2010.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul E. Black, "dual", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 27 December 2010. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/dual.html