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
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 . Also, some relationships between and other domination parameters are established.
V. R. Kulli and Dr. Radha Iyer R., “Inverse total domination in graphs”, Journal of Discrete Mathematical Sciences and Cryptography, vol. 10, pp. 613–620, 2007.