On the variance of Shannon products of graphs

József Balogh, Clifford Smyth

Research output: Contribution to journalArticlepeer-review


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 ℓ-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.

Original languageEnglish (US)
Pages (from-to)110-118
Number of pages9
JournalDiscrete Applied Mathematics
Issue number1
StatePublished - Jan 1 2008


  • Graph product
  • Labeling
  • Variance

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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