More results on weighted independent domination
  Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. In particular, the problem is NP-hard in the classes of sat-graphs and chordal graphs. We strengthen these results by showing that the problem is NP-hard in a proper subclass of the intersection of sat-graphs and chordal graphs. On the other hand, we identify two new classes of graphs where the problem admits polynomial-time solutions. 
Vadim Lozin, Dmitriy Malyshev, Raffaele Mosca, Viktor Zamaraev
cs.DM