Given a nontrivial primitive idempotent E of a distance-regular graph Γ with diameter d⩾ 3,
we obtain an inequality involving the intersection numbers of Γ for each integer i (3⩽ i⩽ d) …

Let Γ denote a bipartite distance-regular graph with diameter D⩾ 4 and valency k⩾ 3. Let θ,
θ′ denote eigenvalues of Γ other than k and− k. We obtain an inequality involving θ, θ …

In this paper, we prove the following two theorems. Theorem 1 Let Γ denote a distance-
regular graph with diameter d≥ 3. Suppose E and F are primitive idempotents of Γ, with …

Let Γ denote a bipartite distance-regular graph with diameter D⩾ 3 and valency k⩾ 3. Γ is
said to be 2-homogeneous whenever for all integers i (1⩽ i⩽ D− 1) and for all vertices x, yz …

Ito, Tanabe and Terwilliger recently introduced the notion of a tridiagonal pair. We apply
their results to distance-regular graphs and obtain the following theorem. Theorem Let Γ …

Let\varGamma Γ be a distance-regular graph with diameter d ≥ 2 d≥ 2. It is said to have
classical parameters (d, b, α, β)(d, b, α, β) when its intersection array {b_0, b_1,\dots, b_ d-1; …

We show that a distance-regular graph Г with Γ (x)≃ 3∗ K a1+ 1 (a 1⩾ 2) for every x∈ Γ and
d⩾ r (Γ)+ 3 is a distance-2 graph of a distance-biregular graph with vertices of valency 3. In …

Let Γ denote a distance-regular graph with diameter d⩾ 2, and fix a vertex x of Γ. Γ is said to
be 1-homogeneous (resp. pseudo-1-homogeneous) with respect to x whenever for all …

Let Γ denote a distance-regular graph with diameter D≥ 3, valency k, and intersection
numbers ai, bi, ci. Let X denote the vertex set of Γ and fix x∈ X. Let Δ denote the vertex …

In this paper, we consider a bipartite distance-regular graph Γ=(X, E) with diameter d≥ 3.
We investigate the local structure ofΓ, focusing on those vertices with distance at most 2 from …