Tight Distance-Regular Graphs and the Q-Polynomial Property |
| |
Authors: | Arlene A. Pascasio |
| |
Affiliation: | (1) Mathematics Department, De La Salle University, 2401 Taft Avenue Manila, Philippines e-mail: cosaap@dlsu.edu.ph, PH |
| |
Abstract: | Let Γ denote a distance-regular graph with diameter d≥3, and assume Γ is tight (in the sense of Jurišić, Koolen and Terwilliger). Let θ denote the second largest or smallest eigenvalue of Γ, and let σ0,σ1,…,σ d denote the associated cosine sequence. We obtain an inequality involving σ0,σ1,…,σ d for each integer i (1≤i≤d−1), and we show equality for all i is closely related to Γ being Q-polynomial with respect to θ. We use this idea to investigate the Q-polynomial structures in tight distance-regular graphs. Received: January 30, 1998 Final version received: August 14, 1998 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|