Dual Graph - Properties

Properties

  • The dual of a plane graph is a plane multigraph - multiple edges.
  • If G is a connected plane graph and if G′ is the dual of G then G is the dual of G′.
  • Since the dual graph depends on a particular embedding, the dual graph of a planar graph is not unique in the sense that the same planar graph can have non-isomorphic dual graphs. In the picture, the red graphs are not isomorphic because the upper one has a vertex with degree 6 (the outer face).

Because of the duality, any result involving counting faces and vertices can be dualized by exchanging them.

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