 
Summary: Asymptotic determination of edgebandwidth of
multidimensional grids and Hamming graphs
Reza Akhtar # Tao Jiang + Zevi Miller #
May 18, 2006
Abstract
The edgebandwidth B # (G) of a graph G is the bandwidth of the line graph of
G. More specifically, for any bijection f : E(G) # {1, 2, . . . , E(G)}, let B # (f, G) =
max{f(e 1 )f(e 2 ) : e 1 and e 2 are incident edges of G}, and let B # (G) = min f B # (f, G).
We determine asymptotically the edgebandwidth of ddimensional grids P d
n and of the
Hamming graph K d
n , the dfold Cartesian product of K n . Our results are as follows.
(1) For fixed d and n # #, B # (P d
n ) = c(d)dn d1 + O(n d 3
2 ), where c(d) is a constant
depending on d, which we determine explicitly.
(2) For fixed even n and d ##, B # (K d
n ) = (1 + o(1))
# d
# 2#
