Distance-regular graphs with Γ(x)≃3∗Ka+1

We show that a distance-regular graph Г with Γ(x) ≃ 3 ∗ Ka1+1 (a1 ⩾ 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 ci, ai, bi (0 ⩽ i ⩽ d) can be denoted by at most four parameters.