Cycle-balance conditions for distance-regular graphs
โ Scribed by Aaron Meyerowitz
- Book ID
- 108315804
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 178 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let F be a distance-regular graph with valency k (k >I 2) and diameter at least 2, and denote by ;t 1 and 2%~m the second largest and least eigenvalue of F, respectively. Assume the multiplicity m( )O of some eigenvalue ;~ ( )~ :/: k) of F satisfies m( Z ) < k. Then ;~ = Z 1 or )'rot. and either (i)
We introduce the retracing argument for distance-regular graphs and prove several results by applying this argument.
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 onl