Note: On explicit formulas for bandwidth and antibandwidth of hypercubes

Authors:
Xiaohan Wang;Xiaolin Wu;Sorina Dumitrescu
Affiliations:
Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada, L8S 4K1;Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada, L8S 4K1;Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, Canada, L8S 4K1
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 6

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New results on edge-bandwidth

Theoretical Computer Science - Selected papers in honor of Lawrence Harper
A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs

Journal of Graph Theory

Index assignment optimization for joint source-channel MAP decoding

IEEE Transactions on Communications
Memetic algorithm for the antibandwidth maximization problem

Journal of Heuristics
On maximum differential graph coloring

GD'10 Proceedings of the 18th international conference on Graph drawing
Variable neighborhood search with ejection chains for the antibandwidth problem

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Antibandwidth and cyclic antibandwidth of Hamming graphs

Discrete Applied Mathematics
Note: Bandwidth of the product of paths of the same length

Discrete Applied Mathematics

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Abstract

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 problem called the antibandwidth of hypercubes. In a recent publication, Raspaud et al. approximated the hypercube antibandwidth up to the third-order term. In this paper, we find the exact value in light of the above recursive structures.