Graph embedding
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation of G {\displaystyle G} on Σ {\displaystyle \Sigma } in which points of Σ {\displaystyle \Sigma } are associated with vertices and simple arcs (homeomorphic images of [ 0 , 1 ] {\displaystyle [0,1]} ) are associated with edges in such a way that: the endpoints of the arc associated with an edge e {\displaystyle e} are the points associated with the end vertices of e , {\displaystyle e,} 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 connected 2 {\displaystyle 2} -manifold.