Fractional dominations and fractional total dominations of graph complements

Let γf(G) and Γf(G) be the fractional domination number and fractional total domination number, resp., of a graph G. We show that γf(G)−1+Γf(Ḡ)−1=1 where Ḡ is the complement of G. This leads to new results for these numbers on the join of graphs, Mycielskiʹs construction, and graph products.