Map (graph theory)

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File:Dodecahedron schlegel.svg

In topology and graph theory, a map is a subdivision of a surface such as the Euclidean plane into interior-disjoint regions,

formed by embedding a graph onto the surface and forming connected components (faces) of the complement of the graph.

That is, it is a tessellation of the surface. A map graph is a graph derived from a map by creating a vertex for each face and an edge for each pair of faces that meet at a vertex or edge of the embedded graph.{{citation|first1=Jonathan|last1=Gross|first2=Jay|last2=Yellen|title=Graph Theory and its applications|year=1998|publisher=CRC Press|isbn=0-8493-3982-0|page=294}}