  Let $G$ be a connected graph with vertex set
$V(G)=\{v_{1},v_{2},...,v_{n}\}$. The distance matrix $D(G)=(d_{ij})_{n\times
n}$ is the matrix indexed by the vertices of $G,$ where $d_{ij}$ denotes the
distance between the vertices $v_{i}$ and $v_{j}$. Suppose that
$\lambda_{1}(D)\geq\lambda_{2}(D)\geq\cdots\geq\lambda_{n}(D)$ are the distance
spectrum of $G$. The graph $G$ is said to be determined by its $D$-spectrum if
with respect to the distance matrix $D(G)$, any graph having the same spectrum
as $G$ is isomorphic to $G$. In this paper, we give the distance characteristic
polynomial of some graphs with small diameter, and also prove that these graphs
are determined by their $D$-spectra.
