Chih-wen Weng

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We prove the following theorem. Theorem. Let Γ = (X, R) denote a distance-regular graph with classical parameters (d, b, α, β) 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) Γ is the dual polar graph 2 A 2d−1 (−b). (ii) Γ is the Hermitian forms graph Her −b (d).(More)
Let G = (V G, EG) be a connected graph on n vertices, with diameter D, adjacency matrix A, and distance function ∂. Assume that A has d + 1 distinct eigenvalues λ 0 > λ 1 > · · · > λ d with corresponding multiplicities m 0 = 1, m 1 ,. . ., m d. From the spectrum of G we then define an inner product ·, ·· on the vector space R d [x] of real polynomials of(More)
Let Γ denote a near polygon distance-regular graph with diameter d ≥ 3, valency k and intersection numbers a 1 > 0, c 2 > 1. Let θ 1 denote the second largest eigenvalue of Γ. We show θ 1 ≤ k − a 1 − c 2 c 2 − 1. We show the following (i)–(iii) are equivalent. (i) Equality is attained above; (ii) Γ is Q-polynomial with respect to θ 1 ; (iii) Γ is a dual(More)
Let Γ denote a distance-regular graph with diameter D ≥ 3, intersection numbers a i , b i , c i and Bose-Mesner algebra M. For θ ∈ C ∪ ∞ we define a 1 dimensional subspace of M which we call M(θ). If θ ∈ C then M(θ) consists of those Y in M such that (A−θI)Y ∈ CA D , where A (resp. A D) is the adjacency matrix (resp. Dth distance matrix) of Γ. If θ = ∞ then(More)
Motivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171–182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs,(More)