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 polyn...

A locating-dominating set D of a graph G is dominating where each vertex not in has unique neighborhood D, and the Locating-Dominating Set problem asks if contains such bounded size. This known to be NP-hard even on restricted classes, as interval graphs, split planar bipartite subcubic graphs. On other hand, it solvable polynomial time for some trees and, more generally, graphs cliquewidth. Wh...