A minus dominating function on a graph  is a labelling  such that  for all  The sum of all labellings of f is the weight of f denoted by  If f is a minus dominating function on G with minimum weight, then its inverse minus dominating function  is a minus dominating function                 on G such that   where  The minimum weight of such a function is the inverse minus domination number of G denoted by  In this paper, we initiate this new type of domination, obtain some properties and characterize the graphs attaining bounds.

domination, minus domination, inverse domination, inverse minus domination