BipartiteQ-Polynomial Distance-Regular Graphs
β Scribed by John S. Caughman IV
- Publisher
- Springer Japan
- Year
- 2004
- Tongue
- English
- Weight
- 319 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
Let 1 denote a bipartite Q-polynomial distance-regular graph with diameter D 4. We show that 1 is the quotient of an antipodal distance-regular graph if and only if one of the following holds. (i) 1 is a cycle of even length. (ii) 1 is the quotient of the 2D-cube. 1999 Academic Press \* , ..., %\
Let be a distance-regular graph with b i = c d-i for all 1 β€ i β€ r. We show that if the diameter d β€ 3r + 2 and a d = 0, then k d = a d + 1 and has two P-polynomial structures.
Let Ξ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (Ξ») > n -1, then D β€ d -1, where P is the polynomial of degree d-1 which takes alternating values Β±1 at Ξ» 1 , . . . , Ξ» d . The graphs satisfying P (Ξ») = n -1, called boundary graphs, h