On \(k\)-dependent domination (Q1598844)

Let \(G = (V,E)\) be a graph and \(D\) a subset of \(V\). We say \(D\) is a dominating set if every vertex of \(V-D\) is adjacent to a vertex in \(D\). It is \(k\)-dependent if the vertices in the subgraph of \(G\) induced by \(D\) have maximum degree \(k\). The authors establish relationships between \(k\)-dependent domination and the standard concepts of domination and irredundance and study related complexity questions.