For every graph $G$ the weak domination number and the independent weak domination number are trivially bounded from above by $|V(G)|-δ(G)$. Similarly, the strong domination number and the independent strong domination number are trivially bounded from above by $|V(G)|-Δ(G)$. The authors study quite simple necessary and sufficient conditions for these domination parameters to attain the given upper bounds. Furthermore, they prove that computing the independent weak domination number and the independent strong domination number for bipartite graphs is NP-hard.
Reviewer: Dieter Rautenbach (Aachen)