This is a wrong answer, as I misread the definition of a dominating set.
Choose $V=\{1,2,\dots\}$ and let the edges be $e_i=\{i,i+1,\dots\}$. The dominating sets are precisely infinite ones.
This is a wrong answer, as I misread the definition of a dominating set.
Choose $V=\{1,2,\dots\}$ and let the edges be $e_i=\{i,i+1,\dots\}$. The dominating sets are precisely infinite ones.