On the Minus Domination Number of Graphs

Abstract

Let G = (V, E) be a simple graph. A 3-valued function Open image in new window is said to be a minus dominating function if for every vertex Open image in new window where N[v] is the closed neighborhood of v. The weight of a minus dominating function f on G is Open image in new window The minus domination number of a graph G, denoted by γ−(G), equals the minimum weight of a minus dominating function on G. In this paper, the following two results are obtained.