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Asymptotic determination of edgebandwidth of multidimensional grids and Hamming graphs
 

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 d-1 + 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#

  

Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)

 

Collections: Mathematics