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Asymptotic determination of edge-bandwidth of multidimensional grids and Hamming graphs
 

Summary: Asymptotic determination of edge-bandwidth of
multidimensional grids and Hamming graphs
Reza Akhtar
Tao Jiang
Zevi Miller
May 18, 2006
Abstract
The edge-bandwidth 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 edge-bandwidth of d-dimensional grids Pd
n and of the
Hamming graph Kd
n, the d-fold Cartesian product of Kn. Our results are as follows.
(1) For fixed d and n , B (Pd
n ) = c(d)dnd-1 + 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))

  

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

 

Collections: Mathematics