Distance-regular graphs of hamming type
β Scribed by Kazumasa Nomura
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 383 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0095-8956
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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 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
This report considers the resistance distance as a recently proposed new ## Ε½ . intrinsic metric on molecular graphs, and in particular, the sum R over resistance distances between all pairs of vertices is considered as a graph invariant. It has been vertices and K denotes a complete graph contai
Let 1=(X, R) denote a distance-regular graph with distance function and diameter d 4. By a parallelogram of length i (2 i d), we mean a 4-tuple xyzu of vertices in X such that (x, y)= (z, u)=1, (x, u)=i, and (x, z)= ( y, z)= ( y, u)=i&1. We prove the following theorem. Theorem. Let 1 denote a distan