# Estimation of DS graph growth

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?

• Haemers conjectures that the proportion of graphs characterized by their spectrum goes to 1 as $n$ increases. And I am wondering how often you expect the topic to be surveyed. – Chris Godsil Dec 26 '11 at 15:21
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