On connected cutfree domination in graphs (Q1200040)

Let \(G=(V,E)\) be a finite connected and undirected graph without loops or multiple edges. For \(S\subseteq V\) let \(\langle S\rangle\) be the subgraph of \(G\) induced by \(S\). \(S\) is a dominating set if every vertex in \(V\backslash S\) is adjacent to some vertex in \(S\). The connected cutfree domination number \(\gamma_{cc}(G)\) is the cardinality of a minimum dominating set \(S\) whereof \(\langle S\rangle\) is cutnode-free. The block domination number \(\gamma_ b(G)\) is the cardinality of a minimum dominating set \(S\), such that \(\langle S\rangle\) is a block of \(G\). \(\gamma_{cc}\) and \(\gamma_ b\) are defined and related to other domination numbers.