Higher rank lamplighter groups are graph automatic
We show that the higher rank lamplighter groups, or Diestel–Leader groups Γd(q) for d≥3, are graph automatic. This introduces a new family of graph automatic groups which are not automatic.
Bérubé, Sophie; Palnitkar, Tara; and Taback, Jennifer, "Higher rank lamplighter groups are graph automatic" (2018). Mathematics Faculty Publications. 45.