Total pitchfork domination and its inverse in graphs

New two domination types are introduced in this paper. Let G = (V,E) be a finite, simple, and undirected graph without isolated vertex. A dominating subset D subset of V (G) is a total pitchfork dominating set if 1 <= vertical bar N(u) boolean AND V - D vertical bar <= 2 for every u is an element of D and G[D] has no isolated vertex. D-1 subset of V - D is an inverse total pitchfork dominating set if D-1 is a total pitchfork dominating set of G. The cardinality of a minimum (inverse) total pitchfork dominating set is the (inverse) total pitchfork domination number (gamma(-t)(pf)(G)) gamma(t)(pf)(G). Some properties and bounds are studied associated with maximum degree, minimum degree, order, and size of the graph. These modified domination parameters are applied on some standard and complement graphs.