2 problems

Let M=(S^3\text{timeshspace{-1.62ex}hspace{-.4ex}hspace{.7ex}}S^1)\#({\mathbb C}{\bf P}^{\,2})^{\# 5}, and let $\text{}^4\hspace{.3pt}15^{\,4}_{\,1}$ denote the specified combi…

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 $n\geq2$…