The graphs with the least distance eigenvalue at least −1+172

Let G be a connected graph with order n and D(G) be the distance matrix of G. Suppose that λ1(D(G))≥⋯≥λn(D(G)) are the distance spectra of G. In this paper, we characterize the graphs with λn(D(G))∈[−1+172,α−1)∪[α−1,−1−2), where α is the smallest root of x3−x2−3x+1=0, and −1+172<α−1<−1−2. Furthermore, we show that the graphs with λn≥−1+172 are determined by their D-spectrum.