  Let $\mathbb{G}_{n,\gamma}$ be the set of simple and connected graphs on $n$
vertices and with domination number $\gamma$. The graph with minimum spectral
radius among $\mathbb{G}_{n,\gamma}$ is called the minimizer graph. In this
paper, we first prove that the minimizer graph of $\mathbb{G}_{n,\gamma}$ must
be a tree. Moreover, for
$\gamma\in\{1,2,3,\lceil\frac{n}{3}\rceil,\lfloor\frac{n}{2}\rfloor\}$, we
characterize all minimizer graphs in $\mathbb{G}_{n,\gamma}$.
