Majority domination in graphs

A two-valued function f defined on the vertices of a graph G = (V, E), f: V → -1, 1, is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. That is, for at least half the vertices v ε{lunate} V, f(N[v]) ≥ 1, where N[v] consists of v and every vertex adjacent to v. The weight of a majority dominating function is f(V) = ∑f(v), over all vertices v ε{lunate} V. The majority domination number of a graph G, denoted γ_maj(G), equals the minimum weight of a majority dominating function of G. In this paper we present properties of the majority domination number and establish its value for various classes of graphs. We show that the decision problem corresponding to the problem of computing γ_maj(G) is NP-complete.