The toroidal crossing number cr_1(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, and a nonplanar graph with toroidal crossing number 0 is called a toroidal graph. A nonplanar graph with toroidal crossing number 0 has graph genus 1 since it can be embedded on a torus (but not in the plane) with no crossings.

graph crossing number | graph genus | graph skewness | Klein bottle crossing number | nonplanar graph | planar graph | projective plane crossing number | rectilinear crossing number | toroidal graph | torus