The genus of a graph G, denoted γ(G) or g(G), is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is embeddable in the plane and is said to be a planar graph. The names of graph classes having particular values for their genera are summarized in the following table. γ | class 0 | planar graph 1 | toroidal graph 2 | double-toroidal graph 3 | pretzel graph Every graph has a genus.

circuit rank | double-toroidal graph | graph crossing number | planar graph | pretzel graph | rectilinear crossing number | toroidal graph