On the nonnegative signed domination numbers in graphs

A nonnegative signed dominating function (NNSDF) of a graph G is a function f from the vertex set V (G) to the set {-1,1} such that ∑_ uє N[v] f(u)≥ 0 for every vertex vєV (G). The nonnegative signed domination number of G, denoted by Y^NN_ s (G), is the minimum weight of a nonnegative signed dominating function on G. In this paper, we establish some sharp lower bounds on the nonnegative signed domination number of graphs in terms of their order, size and maximum and minimum degree.