  Gu et al. in [Inform. Process. Lett. 134 (2018) 52--56] conjectured that the
data center network $D_{k,n}$ is vertex-transitive for all $k\geq0$ and
$n\geq2$. In this paper, we show that $D_{k,n}$ is vertex-transitive for
$k\leq1$ and $n\geq2$, and it is not vertex-transitive for all $k\geq2$ and
$n\geq2$.
