Let D(G) be the distance matrix and let λ 1 (D(G)) ≥ · · · ≥ λ n (D(G)) be the corresponding eigenvalues of a connected graph G. Let m λ (D) denote the multiplicity of the eigenvalue λ of the distance matrix D of G. In this paper, we characterize the graphs with m −2 (D(G)) = n − i, where i = 1, 2, 3, 4. Furthermore, we show that both S + n and S a,b (a + b = n − 2) are determined by their D-spectrum