On the second largest distance eigenvalue of a graph

Let G be a simple connected graph of order n and D(G) be the distance matrix of G. Suppose that zeta(1)(D(G)) >= lambda(2)(D(G)) >= lambda(2) ((D(G)) >= n(D(G)) is the distance spectrum of G. A graph G is said to be determined by its D-spectrum if any graph with the same distance spectrum as G is isomorphic to G. In this paper, we consider spectral characterization on the second largest distance eigenvalue.2(D(G)) of graphs, and prove that the graphs with lambda(2)(D(G)) = 17-v/root 329 2 approximate to -0.5692 are determined by their D-spectra.