Gu et al.'s vertex-transitivity conjecture for Dcell networks

Let $D_{k,n}$ be the data center network Dcell, with $k\geq0$ and $n\geq2$. Gu et al.'s vertex-transitivity conjecture. $D_{k,n}$ is vertex-transitive for all $k\geq0$ and $n\geq2$. The conjecture is false: the paper proves vertex-transitivity for $k\leq1$ and $n\geq2$, but proves that $D_{k,n}$ is not vertex-transitive for all $k\geq2$ and $n\geq2$.