On $Q$-polynomial association schemes of small class

Abstract

We show an inequality involving the third largest or second smallest dual eigenvalues of $Q$-polynomial association schemes of class at least three. Also we characterize dual-tight $Q$-polynomial association schemes of class three. Our method is based on tridiagonal matrices and can be applied to distance-regular graphs as well.

10 pages

References in corpus (1)

• Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes