Abstract
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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Blokhuis, A., Brouwer, A.E. & Haemers, W.H. On 3-chromatic distance-regular graphs. Des. Codes Cryptogr. 44, 293–305 (2007). https://doi.org/10.1007/s10623-007-9100-7
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DOI: https://doi.org/10.1007/s10623-007-9100-7