On the nonnegative signed domination numbers in graphs - Maryam Atapour; Seyyed Mahmoud Sheikholeslami (Electronic Journal of Graph Theory and Applications (EJGTA), 2016)
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 $\sum_{u\in N[v]}f(u)\ge 0$ for every vertex $v\inV(G)$. The nonnegative signed domination number of $G$, denoted by$γ_{s}^{NN}(G)$, 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.