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Ribbon graph

A ribbon graph with one vertex (the yellow disk), three edges (two of them twisted), and one face. It represents an embedding of a graph with three self-loops onto the connected sum of three projective planes.

In topological graph theory, a ribbon graph is a way to represent graph embeddings, equivalent in power to signed rotation systems or graph-encoded maps.[1] It is convenient for visualizations of embeddings, because it can represent unoriented surfaces without self-intersections (unlike embeddings of the whole surface into three-dimensional Euclidean space) and because it omits the parts of the surface that are far away from the graph, allowing holes through which the rest of the embedding can be seen. Ribbon graphs are also called fat graphs.[2]

  1. ^ Cite error: The named reference d was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference fat was invoked but never defined (see the help page).

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