  We show that for all integers $t\geq 8$ and arbitrarily small $\epsilon>0$,
there exists a graph property $\Pi$ (which depends on $\epsilon$) such that
$\epsilon$-testing $\Pi$ has non-adaptive query complexity
$Q=\~{\Theta}(q^{2-2/t})$, where $q=\~{\Theta}(\epsilon^{-1})$ is the adaptive
query complexity. This resolves the question of how beneficial adaptivity is,
in the context of proximity-dependent properties
(\cite{benefits-of-adaptivity}). This also gives evidence that the canonical
transformation of Goldreich and Trevisan (\cite{canonical-testers}) is
essentially optimal when converting an adaptive property tester to a
non-adaptive property tester.
  To do so, we provide optimal adaptive and non-adaptive testers for the
combined property of having maximum degree $O(\epsilon N)$ and being a
\emph{blow-up collection} of an arbitrary base graph $H$.
