The inverse strong non-split r-domination number of a graph

In this paper, we define the notions of inverse strong non-split r-dominating set and inverse strong non-split r-domination number snsr(G) of a graph G. We characterize graphs for which snsr(G) + snsr(G) = n, where snsr(G) is the strong non-split r-domination number of G. We get many bounds on snsr(G). Nordhaus-Gaddum type results are also obtained for this new parameter.