Hardness of r-Dominating Set on Graphs of Diameter (r+1)

A dominating set hits every vertex or one of its neighbours; an r-dominating set only asks that every vertex has something within distance r of it. Finding a small one is W[2]-hard in general. Does small diameter help? On graphs of diameter at most r, a single vertex already r-dominates everything, so the problem is trivial. I show that one extra unit of diameter brings full hardness back: Dominating Set is W[2]-hard on graphs of diameter 2, and r-Dominating Set is W[2]-hard on graphs of diameter r + 1 for every fixed r. The reduction embeds split graphs into a Hamming-graph wireframe and also handles the connected variant.