On linear programming relaxation for ‎k-tuple ‎domination ‎number

For a given graph G=(V,E) , it is proved that finding its domination number and consequently -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 γ_(×K) (G) is obtained. Finaly, these relaxed and integer programming models are utilized to some special graphs and the numerical results are compared