The classification of distance-regular graphs of type IIB
β Scribed by P. Terwilliger
- Publisher
- Springer-Verlag
- Year
- 1988
- Tongue
- English
- Weight
- 313 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We prove the following theorem. Theorem. Let 1=(X, R) denote a distance-regular graph with classical parameters (d, b, :, ;) and d 4. Suppose b<&1, and suppose the intersection numbers a 1 {0, c 2 >1. Then precisely one of the following (i) (iii) holds. (i) 1 is the dual polar graph 2 A 2d&1 (&b).
In [1] N.L. Biggs mentions two parameter sets for distance regular graphs that are antipodal covers of a complete graph, for which existence of a corresponding graph was unknown. Here we settle both cases by proving that one does not exist, while there are exactly two nonisomorphic solutions to the
Let denote a distance-regular graph with diameter D 3. Assume has classical parameters (D, b, Ξ±, Ξ²) with b < -1. Let X denote the vertex set of and let A β Mat X (C) denote the adjacency matrix of . Fix x β X and let A \* β Mat X (C) denote the corresponding dual adjacency matrix. Let T denote the s