, Volume 44, Issue 1-3, pp 293-305,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 28 Jul 2007

On 3-chromatic distance-regular graphs

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.