Recursive Structure and Bandwidth of Hales-Numbered Hypercube
نویسندگان
چکیده
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.
منابع مشابه
On explicit formulas for bandwidth and antibandwidth of hypercubes
The Hales numbered n-dimensional hypercube exhibits interesting recursive structures in n. These structures lead to a very simple proof of the well-known bandwidth formula for hypercubes proposed by Harper, whose proof was thought to be surprisingly difficult. Harper also proposed an optimal numbering for a related problemcalled the antibandwidth of hypercubes. In a recent publication, Raspaud ...
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ورودعنوان ژورنال:
- CoRR
دوره abs/0708.3628 شماره
صفحات -
تاریخ انتشار 2007