Bounding the Diameter of a Distance Regular Graph by a Function of kd, II
โ Scribed by H. Suzuki
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 844 KB
- Volume
- 169
- Category
- Article
- ISSN
- 0021-8693
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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
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
## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and Kovรกcs [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209โ218]. A (ฮด, __g__)โcage is a small