 
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(e1)f(e2) : e1 and e2 are incident edges of G}, and let B (G) = minf B (f, G).
We determine asymptotically the edgebandwidth of ddimensional grids Pd
n and of the
Hamming graph Kd
n, the dfold Cartesian product of Kn. Our results are as follows.
(1) For fixed d and n , B (Pd
n ) = c(d)dnd1 + O(nd 3
2 ), where c(d) is a constant
depending on d, which we determine explicitly.
(2) For fixed even n and d , B (Kd
n) = (1 + o(1))
