For the purposes of
embedding theory, a graph consists of a collection of points, called vertices, certain
pairs of which are joined by homeomorphs of the unit interval, called edges. Edges
may intersect only at vertices, and no vertex is contained in the interior of an edge.
The graph thus becomes a topological space as a subspace of R3. An embedding of a
graph G in a compact 2-manifold (surface) S is then just an embedding of G in S as
a topological space. The genus, γ(G), of G is the minimum genus among all
orientable surfaces into which G may be embedded. The non-orientable genus, γ(G),
is defined analogously. The n-cube, Qn, is a well known graph wnich generalizes
the square and the standard cube. In this paper the following formula is
proven:
