On arithmetic properties of solvable Baumslag-Solitar groups

Laurent Hayez, Tom Kaiser, Alain Valette

For $0<\alpha \le 1$, we say that a sequence $(X_k{)}_{k>0}$ of $d$-regular graphs has property $D_{\alpha }$ if there exists a constant $C>0$ such that $\mathrm{diam}(X_k)\ge C\cdot |X_k{|}^{\alpha }$. We i…