Abstract In this paper, we show that wreath products of groups have linear divergence, and we generalise the argument to permutational wreath products. We also prove that Houghton groups {H}ₘ H m with m 2 m ≥ 2 and Baumslag-Solitar groups have linear divergence. We explain how to generalise the argument for wreath products so that it holds for halo products of groups whose halo is large-scale commutative. Finally, we show that wreath products of graphs and Diestel-Leader graphs have linear divergence. The argument for Diestel-Leader graphs is further generalised to horocyclic products of proper, geodesically complete, Busemann δ -hyperbolic spaces that are uniformly not a quasi-line.
Letizia Issini (Sat,) studied this question.