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
Tight Distance-regular Graphs and the Subconstituent Algebra
β Scribed by Junie T. Go; Paul Terwilliger
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 427 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
An antipodal distance-regular graph of diameter four or five is a covering graph of a connected strongly regular graph. We give existence conditions for these graphs and show for some types of strongly regular graphs that no nontrivial covers exist.
Let 1 be a distance-regular graph of diameter d and valency k>2. If b t =1 and 2t d, then 1 is an antipodal double-cover. Consequently, if f >2 is the multiplicity of an eigenvalue of the adjacency matrix of 1 and if 1 is not an antipodal doublecover then d 2f&3. This result is an improvement of God