Let  be a graph. Let Dbe a minimum neighborhood total dominating set of G. If  contains a neighborhood total dominating set  of G, then  is called an inverse neighborhood total dominating set with respect to D. The inverse neighborhood total domination number  of Gis the minimum cardinality of an inverse neighborhood total dominating set of G. The disjoint neighborhood total domination number  of a graph Gis the minimum cardinality of the union of two disjoint neighborhood total dominating sets in G. In this paper, we initiate a study of these new parameters.

inverse neighborhood total dominating set, inverse neighborhood total domination number, disjoint neighborhood total domination number.