For a given graph G = (V, E) , it is proved that finding its domination number (G) and consequently k -tuple domonation number is an NP-complete problem. In this paper, first a linear integer programming model is presented to find the k -tuple dominating set. Then, the linear relaxation is applied to this integer programming model and an approximation of the k -tuple domonation number k (G) is obtained. Finaly, these relaxed and integer programming models are utilized to some special graphs and the numerical results are compared.
