Recursive Structure and Bandwidth of Hales-Numbered Hypercube

Details Recursive Structure and Bandwidth of Hales-Numbered Hypercube Recursive Structure and Bandwidth of Hales-Numbered Hypercube

2007-08-27

arxiv.org/abs/0708.3628v1

Computer Science

Discrete Mathematics

10 pages

Scientific paper

The Hales numbered $n$-dimensional hypercube and the corresponding adjacency matrix exhibit interesting recursive structures in $n$. These structures lead to a very simple proof of the well-known bandwidth formula for hypercube, whose proof was thought to be surprisingly difficult. A related problem called hypercube antibandwidth, for which Harper proposed an algorithm, is also reexamined in the light of the above recursive structures, and a close form solution is found.

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