Least domination in a graph (Q1916102)

The least domination number \(\gamma_L\) of a graph \(G\) is the minimum cardinality of a dominating set \(D\) of \(G\) such that the domination number of the graph induced by \(D\) is a minimum. The least point covering number \(\alpha_L\) of a graph \(G\) is the minimum cardinality of a total point cover \(S\) of \(G\) (a point cover that includes all isolated points of \(G\)) such that the total point cover number of the subgraph induced by \(S\) is a minimum. The author shows, among their things, that if \(G\) is a graph of order \(n\geq 2\) with no isolated points, then \(\gamma_L\leq {3\over 5} n\) and \(\gamma_L\leq {3\over 2} \alpha_L\).