On The Bandwidth Of A Hamming Graph

The bandwidth of the Hamming graph (the product, (K-n)(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 (K-n)(d) is asymptotic to root(2/pid)n(d) as d --> infinity. (C) 2003 Published by Elsevier Science B.V.