In topological graph theory, an embedding (also spelled imbedding) of a graph on a surface is a representation of on in which points of are associated with vertices and simple arcs (homeomorphic images of ) are associated with edges in such a way that: * the endpoints of the arc associated with an edge are the points associated with 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 -manifold.