A new inequality for distance-regular graphs

✍ Scribed by Paul Terwilliger

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 521 KB
• Volume: 137
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)e0170-9

✦ Synopsis

Given a nontrivial primitive idempotent E of a distance-regular graph/-with diameter d ~> 3, we obtain an inequality involving the intersection numbers of F for each integer i (3 ~< i ~< d). We show equality is attained for i = 3 if and only if equality is attained for all i (3 ~< i ~< d) if and only if F is Q-polynomial with respect to E. If the intersection numbers of F are such that qci-bi-q(qci-l-bi-l) is independent ofi (l ~<i~<d) for some q ~ ~",,, {0, -1] (as is the case for many examples), our inequalities take an especially simple form.