On a Distance-Regular Graph of Even Height with ke = kf
โ Scribed by Hiroshi Nakano
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 117 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
and Terwilliger recently introduced the notion of a tridiagonal pair. We apply their results to distance-regular graphs and obtain the following theorem. THEOREM. Let denote a distance-regular graph with diameter D โฅ 3. Suppose is Q-polynomial with respect to the ordering E 0 , E 1 , . . . , E D of
Let [' be a distance regular graph with intersection array {bo, bl, . โข., bd\_l; ct, ..., ed}. It is shown that in same cases (c i 1, ai-I, br I) = (ct, at, bt) and (c2~ t, a2~ 1, b2i l) = (ci, a~, bi) imply k <\_ 2b i + 1. As a corollary all distance regular graphs of diameter d = 3i -1 with b I =
Bannai and Ito conjectured in a 1987 paper that there are finitely many distance-regular graphs with fixed degree that is greater than two. In a series of papers they showed that their conjecture held for distance-regular graphs with degrees 3 or 4. In this paper we prove that the Bannai-Ito conject