A remark on bipartite distance-regular graphs of even valency
โ Scribed by K. Nomura
- Publisher
- Springer Japan
- Year
- 1995
- Tongue
- English
- Weight
- 104 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
In this paper, we consider a bipartite distance-regular graph = (X, E) with diameter d โฅ 3. We investigate the local structure of , focusing on those vertices with distance at most 2 from a given vertex x. To do this, we consider a subalgebra R = R(x) of Mat X (C), where X denotes the set of vertice
Let 1 denote a 2-homogeneous bipartite distance-regular graph with diameter D 3 and valency k 3. Assume that 1 is not isomorphic to a Hamming cube. Fix a vertex x of 1, and let T=T(x) denote the Terwilliger algebra of T with respect to x. We give three sets of generators for T, two of which satisfy
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 =