Induced-paired domination in graphs. (Q2715977)

A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). If moreover the subset \(\langle S\rangle \) of \(G\) induced by \(S\) consists of independent edges, then \(S\) is an induced-paired dominating set in \(G\). The minimum number of vertices of such a set is the induced-paired domination number \(\gamma _{ip}(G)\) of \(G\). Its properties are studied. Section titles: Complexity, Bounds, Existence results, Trees, Caterpillars.