1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs
نویسندگان
چکیده
منابع مشابه
Pseudo 1-homogeneous distance-regular graphs
Let be a distance-regular graph of diameter d ≥ 2 and a1 = 0. Let θ be a real number. A pseudo cosine sequence for θ is a sequence of real numbers σ0, . . . , σd such that σ0 = 1 and ciσi−1 + aiσi + biσi+1 = θσi for all i ∈ {0, . . . , d−1}. Furthermore, a pseudo primitive idempotent for θ is Eθ = s ∑di=0 σiAi , where s is any nonzero scalar. Let v̂ be the characteristic vector of a vertex v ∈ V...
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Let Γ be a distance-regular graph with diameter d. For vertices x and y of Γ at distance i, 1 ≤ i ≤ d, we define the sets Ci(x, y) = Γi−1(x) ∩ Γ(y), Ai(x, y) = Γi(x) ∩ Γ(y) and Bi(x, y) = Γi+1(x) ∩ Γ(y). Then we say Γ has the CABj property, if the partition CABi(x, y) = {Ci(x, y), Ai(x, y), Bi(x, y)} of the local graph of y is equitable for each pair of vertices x and y of Γ at distance i ≤ j. ...
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Let Γ denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3 and intersection numbers ci , bi (0 ≤ i ≤ D). By a pseudo cosine sequence of Γ we mean a sequence of scalars σ0, . . . , σD such that σ0 = 1 and ciσi−1 + biσi+1 = kσ1σi for 1 ≤ i ≤ D − 1. By an associated pseudo primitive idempotent we mean a nonzero scalar multiple of the matrix ∑D i=0 σi Ai , where A0, . . . , ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2005
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2004.10.003