We know that $DS$ graphs are such connected graphs that determinable by their adjacency spectrum.

Suppose $DS(n)$ and $G(n)$ show the number of $DS$ graphs and all graphs with $n$ vertices,respectively.

$1)$ Do we have any good approximation for $DS(n)$(even if $n$ be sufficiently large)?

$2)$ what is the behavior of $\alpha$, if we have:

$lim (DS(n)/ (G(n)-DS(n))^\alpha=c\neq0)$

$n \rightarrow \infty$

Is there any new survey about DS graphs, after 2010?