A Lower Bound on Minus Domination Number of a Graph

Let G=(V,E) be a simple graph,define a function f:V→{-1,0,+1},the function f is a minus domination function of G if every vertex x∈V(G),the closed neighborhood N[x] of x contains more vertices with function value +1 than with-1.The minus domination number of G,denote by γ-(G),is the minimum weight of a minus domination function on G.In this paper,a sharp lower bound on the minus domination number of a general graph with order n minimum degree δ and maximum degree Δ is given:It is shown that the main result in paper [7] is a special example of the lower bound from this paper.