Dominating sets reconfiguration under token sliding

Let G be a graph and Ds Dt two dominating sets of size k. Does there exist sequence 〈D0=Ds,D1,…,Dℓ−1,Dℓ=Dt〉 such that Di+1 can obtained from Di by replacing one vertex with its neighbors? In this paper, we investigate the complexity decision problem. We first prove problem is PSPACE-complete, even when restricted to split, bipartite or bounded treewidth graphs. On other hand, it solved in polynomial time on dually chordal graphs (a superclass both trees interval graphs) cographs.