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The Genus of the n-Cube

Published online by Cambridge University Press:  20 November 2018

Lowell W. Beineke  and
Frank Harary
Lowell W. Beineke
Affiliation:
The University of Michigan and University College, London
Frank Harary
Affiliation:
The University of Michigan and University College, London
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 494 - 496
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Beineke, L. W. and Harary, F., Inequalities involving the genus of a graph and its thicknesses. Proc. Glasgow Math. Assoc. (1965), to appear.Google Scholar
2. König, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936; reprinted New York, 1950).Google Scholar