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 $n\geq2$.
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