Exact Algorithms for r-Dominating Set on Bounded Treewidth Graphs Given a graph, $G = (V, E)$, I want to find an optimal $r$-domination for $G$. That is, I want a subset $S$ of $V$ such that all vertices in $G$ are at a distance of at most $r$ from some vertex in $S$, while minimizing the size of $S$. 

From what I have checked so far, I got the following: There is this related problem of finding a $(k,r)$-center in a graph which is a subset $S$ of size at most $k$ such that all the vertices in the graph are at a distance of atmost $r$ from some vertex in $S$(here both $|S| \leq k$ and $r$ are parts of the input) for which Demaine et al. have a FPT algorithm for planar graphs. Otherwise the problem is $W[2]$-hard for even $r = 1$.

Is anything known about the exact complexity of $r$-domination problem for bounded tree width graphs or even just trees? (Is $r$-domination MSO definable? the usual $k$-dominating set problem is MSO definable -- which then would allow one to use Courcelle's theorem to conclude that there is a linear time algorithm for the problem). Are there any conditional hardness results known regarding this problem?
An (optimal) $r$-domination for $G$ is an (optimal) domination for the $r$th power $G^r$ and vice versa 
($G^r$ is obtained from $G$ by adding new edges between distinct vertices of distance at most $r$).

The following facts are well known: (1) All powers of a strongly chordal graph are strongly chordal 
(A. Lubiw, Master thesis; see also Dahlhaus &amp; Duchet, On strongly chordal graphs, 
Ars Combin. 24 B (1987) 23-30), and (2) Domination is solvable in linear time for strongly chordal graphs 
(M. Farber. Domination, independent domination and duality in strongly chordal graphs, 
Discrete Appl. Math., 7 (1984) 115–130). Hence $r$-domination is solvable in polynomial time for 
strongly chordal graphs, in particular for trees ($r$ fixed or not).

Gurski &amp; Wanke proved in this paper 
that the clique-width of $G^r$ is at most $2\cdot (r+1)^{\text{tw}(G)+1}−2$, where $\text{tw}(G)$ is the tree-width 
of $G$. Thus, for fixed $r$, the $r$th powers of bounded tree-width graphs have bounded clique-width. 
Hence, for fixed $r$, $r$-domination is solvable in polynomial time for bounded tree-width graphs 
(by Courcelle's theorem).