Dual graphs are those, where for a planar graph G, the graph has a vertex for each plane region of G. Dual graphs are highly complex mathematical concepts which require skill and considerable study in order to grasp them. Self dual graphs are also a subgroup of dual graphs. Some their important properties are as follows:
The dual graph H for a planar graph G must be drawn in a way that G is also the dual graph of H. This makes dual graphs symmetric and this is why they have been given the name of dual graphs.
Dual graphs are often used to represent RNA. This is an interesting use of dual graphs which is inter-generic. Biological functions are also often represented with the help of dual graphs.
Dual graphs are highly technical and thus they are only used for academic purposes or in very specialized fields. They should be correctly written keeping in mind the complex mathematical equations involving planar graphs.
Dual graphs of planar graphs are also known as planar multigraphs. Combinatorial dual graphs are also part of this group of specialized graphs. Dual graphs must be labeled correctly; otherwise they are ambiguous and meaningless.
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