Graph embedding

In topological graph theory, an embedding (also spelled imbedding) of a graph  on a surface S is a representation of on S in which points of S are associated to vertices and simple arcs (homeomorphic images of [0,1]) are associated to edges in such a way that:

• the endpoints of the arc associated to an edge are the points associated to the end vertices of ,
• no arcs include points associated with other vertices,
• two arcs never intersect at a point which is interior to either of the arcs.

Here a surface is a compact, connected 2-manifold.