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?



Estimation of DS graph growth
As far as I know, the computation of these values up to 11 vertices by van Dam and Haemers is still the best result. No asymptotics are known.


