On the nonnegative signed domination numbers in graphs - Maryam Atapour; Seyyed Mahmoud Sheikholeslami (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2016)
A nonnegative signed dominating function (NNSDF) of a graph Gis a function f from the vertex set V(G) to the set {-1,1}such that _uN[v]f(u)0 for every vertex v(G). The nonnegative signed domination number of G, denoted byγ_s^NN(G), is the minimum weight of a nonnegativesigned dominating function on G. In this paper, we establishsome sharp lower bounds on the nonnegative signed dominationnumber of graphs in terms of their order, size and maximum andminimum degree.