  Let $G_{n,\gamma}$ be the set of all connected graphs on $n$ vertices with
domination number $\gamma$. A graph is called a minimizer graph if it attains
the minimum spectral radius among $G_{n,\gamma}$. Very recently, Liu, Li and
Xie [Linear Algebra and its Applications 673 (2023) 233--258] proved that the
minimizer graph over all graphs in $\mathbb{G}_{n,\gamma}$ must be a tree.
Moreover, they determined the minimizer graph among
$G_{n,\lfloor\frac{n}{2}\rfloor}$ for even $n$, and posed the conjecture on the
minimizer graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$. In this
paper, we disprove the conjecture and completely determine the unique minimizer
graph among $G_{n,\lfloor\frac{n}{2}\rfloor}$ for odd $n$.
