A graph with its edges labeled either as positive or negative is called a signed graph. Denoting  to be the open neighbourhood of a vertex u, if  is a signed graph, a subset  of vertices of  is a dominating set, if there exists a marking    of  such that every vertex u of  is either in D or whenever  and  for every  A dominating set D of  is called a minimal dominating set if no proper subset of D becomes a dominating set. In this paper, we mainly characterize minimal dominating sets for signed graphs along with some other important results on domination for signed graphs. We also discuss briefly on the bounds for the domination number of signed graphs.

signed graph, domination, dominating set, independent set, irredundant set.