Connected k-dominating graphs

We present two related constructions. The first construction shows that for each integer k≥3 and each integer r such that 1≤r≤k−1, there exists a graph Gk,r such that Γ(Gk,r)=k, γ(Gk,r)=r+1 and d0(Gk,r)=k+r=Γ(G)+γ(G)−1. The second construction shows that for each integer k≥3 and each integer r such that 1≤r≤k−1, there exists a graph Qk,r such that Γ(Qk,r)=k, γ(Qk,r)=r and d0(Qk,r)=k+r=Γ(G)+γ(G).