Acyclic domination
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 subgraph \(\langle S\rangle\) of \(G\) induced by \(S\) contains no circuit, then \(S\) is an acyclic dominating set in \(G\). The minimum number of vertices of an acyclic dominating set in \(G\) is the acyclic domination number \(\gamma_a(G)\) of \(G\). In the paper this number is studied and compared with other numerical invariants of graphs concerning domination, mainly with the upper irredundance number \(\text{IR}(G)\) and the lower independence number \(\text{ir}(G)\).
scientific article; zbMATH DE number 1506824