An inequality on the cosines of a tight distance-regular graph Original Research Article

Let Γ denote a distance-regular graph with diameter dgreater-or-equal, slanted3, and assume Γ is tight in the sense of Juriimageiimage et al. [J. Algebraic Combin. 12 (2000) 163–197]. Let θ denote the second largest or the smallest eigenvalue of Γ. We obtain an inequality involving the first, second and third cosines associated with θ. We investigate the relationship between equality being attained and the existence of dual bipartite Q-polynomial structures on Γ.