Geodesic
On the connectedness of the complement of a ball in distance-regular graphs
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 191-195.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: An important property of strongly regular graphs is that the second subconstituent of any primitive strongly regular graph is always connected. Brouwer asked to what extent this statement can be generalized to distance-regular graphs. In this paper, we show that if $\gamma $ is any vertex of a distance-regular graph $\Gamma $ and t is the index where the standard sequence corresponding to the second largest eigenvalue of $\Gamma $ changes sign, then the subgraph induced by the vertices at distance at least t from $\gamma $, is connected.
Keywords: distance-regular graph, strongly regular graph, subconstituent, connectivity, eigenvalue, standard sequence 
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Cioabă, Sebastian M.; Koolen, Jack H. On the connectedness of the complement of a ball in distance-regular graphs. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 191-195. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a2/