Minus domination in regular graphs

A three-valued function f defined on the vertices of a graph G = (V,E), f : V , ( 1 , 0 , 1), is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v E V, f(N[v])>~ 1, where N[v] consists of v and every vertex adjacent to v. The weight of a minus dominating function is f ( V ) = ~ f (v) , over all vertices v E V. The minus domination number of a graph G, denoted 7-(G), equals the minimum weight of a minus dominating function of G. In this note, we establish a sharp lower bound on 7(G) for regular graphs G.