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=(X, R) denote a distance-regular graph with diameterD≥ 3 and distance functionδ. A
(vertex) subgraph Δ⊆ Xis said to beweak-geodetically closedwhenever for allx, y∈ Δ and …

A note on triangle-free distance-regular graphs with a2≠0 Page 1 Journal of Combinatorial
Theory, Series B 99 (2009) 266–270 Contents lists available at ScienceDirect Journal of …

Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D≥ 3.
Assume the intersection numbers a1= 0 and a2≠ 0. We show that Γ is 3-bounded in the …

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; …

Distance-regular Subgraphs in a Distance-regular Graph , III Page 1 Europ . J .
Combinatorics (1996) 17 , 629 – 636 Distance-regular Subgraphs in a Distance-regular …

Let Г be a distance-regular graph of valency k≥ 3 and diameter d. Suppose the intersection
array has t columns different from t (1, 0, k− 1). Then it is shown that d is bounded from …

Let Γ denote a distance-regular graph with diameter d≥ 3. By a parallelogram of length 3,
we mean a 4-tuple xyzw consisting of vertices of Γ such that∂(x, y)=∂(z, w)= 1,∂(x, z)= 3 …

Let Γ be a distance-regular graph of diameter d≥ 3 with c 2> 1. Let m be an integer with 1≤
m≤ d− 1. We consider the following conditions:(SC) m: For any pair of vertices at distance m …

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 …