Dominating set of given size $k$ in $O(2^k |V| |E|)$

Recently I’ve encountered an interesting case of dominating set problem: given an unweighted and undirected graph $ G(V, E)$ and knowing that it contains a dominating set of size $ k$ , find any such dominating set in time $ O(2^k\ \vert V \vert\ \vert E \vert)$ .

During my research, I found only some algorithms to find fixed-size dominating set in a $ d$ -degenerated graphs, but no such restriction is applied in this problem.

Is there any way to solve that problem in such time?