I have a found a small article  saying (the first paragraph of the introduction) that the minimum-weight independent dominating set is NP-complete in chordal graphs, but at the same time, seems to contradict that exact statement.
Moreover, I have found another reference  saying that in chordal graphs, it is polynomial time solvable. So which one is it?
Note: I am just trying to reference this result in a project of mine. No need for a proof.
Edit: I am referring to this piece of the introduction: "Domination and most of its variations are NP-complete for chordal graphs (even for the subclass of split graphs) with the exception of independence domination (see ). On the other hand, an unpublished proof for the NP-completeness of the weighted independent domination in chordal graphs by the author 20 years ago..." Then in my reference , it also states that the weighted version is polynomial time solvable, yet here they say that there is an NP-completeness proof. Am I missing something fundamental?
- The weighted independent domination problem is NP-complete for chordal graphs by G. J. Chang (2004)
- Fundamentals of Domination in Graphs by T. W. Haynes, S. Hedetniemi and P. Slater (1998)