Width and dual width of subsets in polynomial association schemes (Q1395814)

The width of a subset \(C\) of the vertices of a distance-regular graph is the maximum distance which occurs between elements of \(C\). Dually, the dual width of a subset in a cometric association scheme is the index of the ``last'' eigenspace in the Q-polynomial ordering to which the characteristic vector of \(C\) is not orthogonal. Two simple bounds are derived on these two new parameters. The authors show that any subset of minimal width is a completely regular code and that any subset of minimal dual width induces a cometric association scheme in the original. A rather inclusive list of examples and applications is given.