Let denote a bipartite distance-regular graph with diameter D¿4 and valency k¿3. Let ; ′ denote eigenvalues of other than k and −k. We obtain an inequality involving ; ′ and the intersection numbers… (More)

Let 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 . For 0 ≤ i ≤ D, let Ei… (More)

We consider a bipartite distance-regular graph Γ with diameter D ≥ 4, valency k ≥ 3, intersection numbers bi, ci, distance matrices Ai, and eigenvalues θ0 > θ1 > · · · > θD. Let X denote the vertex… (More)

Considering Canada's Tri-Council statement on the ethical conduct for research involving human subjects, we discuss some of the ethical challenges of doing research on teaching and learning in which… (More)

Let G denote a bipartite distance-regular graph with diameter DX4; valency kX3; and Bose–Mesner algebra M: Let y04y14?4yD denote the distinct eigenvalues for G; and for 0pipD; let Ei denote the… (More)

We consider a bipartite distance-regular graph Γ with vertex set X, diameter D ≥ 4, and valency k ≥ 3. For 0 ≤ i ≤ D, let Γ i (x) denote the set of vertices in X that are distance i from vertex x. We… (More)

We consider a bipartite distance-regular graph Γ with diameter D ≥ 4 and valency k ≥ 3. Let X denote the vertex set of Γ and fix x ∈ X. Let Γ22 denote the graph with vertex set X̆ = {y ∈ X | ∂(x, y)… (More)

Weconsider a bipartite distance-regular graphΓ with vertex setX , diameterD ≥ 4, and valency k ≥ 3. Let CX denote the vector space over C consisting of column vectors with rows indexed by X and… (More)