Distance-regular graphs with [formula omitted

Abstract

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 particular, intersection numbers c i , a i , b i (0 ⩽ i ⩽ d) can be denoted by at most four parameters.