Designs, Codes and Cryptography

, Volume 44, Issue 1, pp 293–305

On 3-chromatic distance-regular graphs

  • Aart Blokhuis
  • Andries E. Brouwer
  • Willem H. Haemers
Open AccessArticle

DOI: 10.1007/s10623-007-9100-7

Cite this article as:
Blokhuis, A., Brouwer, A.E. & Haemers, W.H. Des. Codes Cryptogr. (2007) 44: 293. doi:10.1007/s10623-007-9100-7


We give some necessary conditions for a graph to be 3-chromatic in terms of the spectrum of the adjacency matrix. For all known distance-regular graphs it is determined whether they are 3-chromatic. A start is made with the classification of 3-chromatic distance-regular graphs, and it is shown that such graphs, if not complete 3-partite, must have λ ≤ 1.


Distance-regular graphsChromatic number

AMS Classification

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Aart Blokhuis
    • 1
  • Andries E. Brouwer
    • 1
  • Willem H. Haemers
    • 2
  1. 1.Department of MathematicsTechnological University EindhovenEindhovenThe Netherlands
  2. 2.Department of Econometrics & O.R.Tilburg UniversityTilburgThe Netherlands