On the bandwidth of a Hamming graph

Authors:
L. H. Harper
Affiliations:
Department of Mathematics, University of California, Riverside, Riverside, CA
Venue:
Theoretical Computer Science
Year:
2003

Citing 2
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Abstract

The bandwidth of the Hamming graph (the product, (Kn)d, of complete graphs) has been an open question for many years. Recently Berger-Wolf and Rheingold [1] pointed out that the bandwidth of a numbering of the Hamming graph may be interpreted as a measure of the effects of noise in the multi-channel transmission of data with that numbering. They also gave lower and upper bounds for it. In this paper we present better lower and upper bounds, showing that the bandwidth of Kn)d is asymptotic to √(2/πd)nd as d → ∞.