Note: On the variance of Shannon products of graphs

Authors:
József Balogh;Clifford Smyth
Affiliations:
University of Illinois at Urbana-Champaign, IL 61801, USA;MIT, Boston, MA, USA
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 5
Cited 2

Some intersection theorems for ordered sets and graphs

Journal of Combinatorial Theory Series A
On the bandwidth of a Hamming graph

Theoretical Computer Science
Edge-isoperimetric problems for Cartesian powers of regular graphs

Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Index assignment for two-channel quantization

IEEE Transactions on Information Theory
Design of multiple description scalar quantizers

IEEE Transactions on Information Theory

On the bandwidth of 3-dimensional Hamming graphs

Theoretical Computer Science
Note: Bandwidth of the product of paths of the same length

Discrete Applied Mathematics

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Abstract

We study the combinatorial problem of finding an arrangement of distinct integers into the d-dimensional N-cube so that the maximal variance of the numbers on each @?-dimensional section is minimized. Our main tool is an inequality on the Laplacian of a Shannon product of graphs, which might be a subject of independent interest. We describe applications of the inequality to multiple description scalar quantizers (MDSQ), to get bounds on the bandwidth of products of graphs, and to balance edge-colorings of regular, d-uniform, d-partite hypergraphs.