Inverse total domination in graphs

Let G = (V, E) be a graph. Let D be a minimum total dominating set of G. If V - D contains a total dominating set D' of G, then D' is called an inverse total dominating set with respect to D. The inverse total domination number gamma(t)'(G) of G is the minimum number of vertices in an inverse total dominating set of G. We initiate the study of inverse total domination in graphs and present some bounds and some exact values for gamma(t)'(G). Also, some relationships between gamma(t)'(G) and other domination parameters are established.