The Genus of the n-Cube
Lowell W. Beineke, Frank Harary · Canadian Journal of Mathematics · 1965
The definition of the genus γ(G) of a graph G is very well known (König 2): it is the minimum genus among all orientable surfaces in which G can be drawn without intersections of its edges. But there are very few graphs whose genus is known. The purpose of this note is to answer this question for one family of graphs by determining the genus of the n-cube. The graph Qn called the n-cube has 2n vertices each of which is a binary sequence a1a2. . . an of length n, where ai = 0 or 1.