We show that the following are equivalent: (i) θ , θ ′ satisfy equality in BFB; (ii) the entry-wise product E ∘ F is a linear combination of at most two primitive idempotents of Γ .Expand

AbstractLet Γ denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3, and distinct eigenvalues θ0 > θ1 > ··· > θD. Let M denote the Bose-Mesner algebra of Γ. For 0 ≤ i ≤ D, let… Expand

We consider a bipartite distance-regular graph @C with diameter D>=4, valency k>=3, intersection numbers b"i,c" i, distance matrices A"i-i, and eigenvalues @q"0>@q"1>...>@Q"D.Expand

Abstract Let Γ denote a bipartite distance-regular graph with diameter D ≥ 4 and valency k ≥ 3 . Let X denote the vertex set of Γ, and let A denote the adjacency matrix of Γ. For x ∈ X let T = T ( x… Expand

Abstract Let Γ denote a bipartite distance-regular graph with diameter D ≥ 4 and valency k ≥ 3 . Let X denote the vertex set of Γ, and let A denote the adjacency matrix of Γ. For x ∈ X and for 0 ≤ i… Expand

We consider a bipartite distance-regular graph ΓΓ with vertex set XX, diameter D≥ 4D≥4, valency k≥ 3k≥3, and eigenvalues θ0>θ1>⋯> θD, and show that the graph is taut if and only if Δ≠0Δ≠ 0.Expand