On Nonnegative Signed Domination in Graphs and its Algorithmic Complexity

Let G = (V, E) be a simple graph with vertex set V and edge set E. A function f from V to a set {-1, 1} is said to be a nonnegative signed dominating function (NNSDF) if the sum of its function values over any closed neighborhood is at least zero. The weight of f is the sum of function values of vertices in V. The nonnegative signed domination number for a graph G equals the minimum weight of a nonnegative signed dominating function of G. In this paper, exact values are found for cycles, stars, wheels, spiders and complete equally bipartite graphs and we present some lower bounds for nonnegative signed domination number in terms of the order and the maximum and minimum degree. Fothermore, we show that the decision problem corresponding to the problem of computing the nonnegative signed domination number is NP-complete.