Cellular Embedding

A cellular embedding of a graph in a surface is a graph embedding in which every face is homeomorphic to an open disk. Cellular embeddings are useful in topological graph theory because the vertices, edges, and graph faces determine the surface genus using the Euler characteristic. An orientable rotation system determines a cellular embedding of a connected graph.

See also

Graph Embedding, Graph Face, Genus, Rotation System, Surface, Topological Graph Theory

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References

Gross, J. L. and Tucker, T. W. Topological Graph Theory. New York: Wiley, 1987.Mohar, B. and Thomassen, C. Graphs on Surfaces. Baltimore, MD: Johns Hopkins University Press, 2001.

Cite this as:

Weisstein, Eric W. "Cellular Embedding." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CellularEmbedding.html

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