In topological graph theory, an embedding 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 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. Wikipedia