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Taut distance-regular graphs and the subconstituent algebra
TLDR
We consider a bipartite distance-regular graph @C with diameter D>=4 and valency k>=3. Expand
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An inequality involving two eigenvalues of a bipartite distance-regular graph
TLDR
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
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Taut Distance-Regular Graphs of Odd Diameter
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, letExpand
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The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme
TLDR
We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. Expand
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The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two
TLDR
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
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On bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint two
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 ( xExpand
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On the Terwilliger algebra of bipartite distance-regular graphs with Δ2 = 0 and c2 = 1
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 ≤ iExpand
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Taut distance-regular graphs of even diameter
  • Mark S. MacLean
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1 May 2004
TLDR
We show that a distance-regular graph with even diameter is taut if and only if it has at least one taut pair of primitive idempotents. Expand
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A new approach to the Bipartite Fundamental Bound
TLDR
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
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A new characterization of taut distance-regular graphs of odd diameter
TLDR
We consider a bipartite distance-regular graph @C with vertex set X, diameter D>=4, and valency k>=3. Expand
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