A remark on the intersection arrays of distance regular graphs and the distance regular graphs of diameter d = 3i − 1 with b _i = 1 and k > 2

Abstract

Let Γ be a distance regular graph with intersection array b ₀, b ₁,..., b _d−1; c ₁,..., c _d. It is shown that in some cases (c _i−1, a _i−1, b _i−1) = (c ₁, a ₁, b ₁)and (c _2i−1, a _2i−1, b _2i−1) imply k ≤ 2b _i + 1. As a corollary all distance regular graphs of diameter d = 3i − 1 with b _i = 1 and k > 2 are determined.