\noindent Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0. \mathscr{C}_1$ and $\mathscr{C}_2$. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class $\mathscr{C}_2$. Of interest. https://www.spidertattooz.com/UMA-Sound-Lantern/