Let $H$ be a hereditary algebra of Dynkin type $D_n$ over a field $k$ and
$\mathscr{C}_H$ be the cluster category of $H$. Assume that $n\geq 5$ and that
$T$ and $T'$ are tilting objects in $\mathscr{C}_H$. We prove that the
cluster-tilted algebra $\Gamma=\mathrm{End}_{\mathscr{C}_H}(T)^{\rm op}$ is
isomorphic to $\Gamma'=\mathrm{End}_{\mathscr{C}_H}(T')^{\rm op}$ if and only
if $T=\tau^iT'$ or $T=\sigma\tau^jT'$ for some integers $i$ and $j$, where
$\tau$ is the Auslander-Reiten translation and $\sigma$ is the automorphism of
$\mathscr{C}_H$ defined in section 4.

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and
$A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$,
we denote by $\delta (T)$ the number of non isomorphic indecomposable summands
of $T$. In this paper, we prove that a partial tilting $A^{(m)}$-module $T$ is
a tilting $A^{(m)}$-module if and only if $\delta (T)=\delta (A^{(m)})$, and
that every partial tilting $A^{(m)}$-module has complements. As an application,
we deduce that the tilting quiver $\mathscr{K}_{A^{(m)}}$ of $A^{(m)}$ is
connected.