Calculating the domination number is an NPHard problem. Does it remain NPHard if we restrict it to nonbipartite graphs?

The general case of the domination number problem reduces to the nonbipartite case. Given a (possibly bipartite graph) $G$, create new graph $G'$ consisting of an copy of $G$ and a disjoint copy of $K_3$. The domination number of the new (nonbipartite) graph $G'$ is exactly one more than that of the original graph $G$. So computing the domination number of the new graph $G'$ is exactly as hard as computing that of the original graph $G$. 

