On the conjecture of vertex-transitivity of Dcell

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 $k\ge 0$ and $n\ge 2$. In this paper, we show that $D_{k,n}$ is vertex-transitive for $k\le 1$ and $n\ge 2$, and it is not vertex-transitive for all $k\ge 2$ and $n\ge 2$.