Fractional dominations and fractional total dominations of graph complements (Q1613430)

Let \(\gamma_f(G)\) and \(\Gamma_f(G)\) be the fractional domination number and the fractional total domination number of a graph \(G\). If \(\overline G\) is the complement of \(G\), then the main result says that \({\gamma_f(G)}^{-1}+ {\Gamma_f(\overline G)}^{-1}=1.\) As an application of this identity, the author presents results for these parameters on the join of graphs, Mycielski's construction, and some graph products.