Signed domination numbers of a graph and its complement

Let G=(V,E) be a simple graph on vertex set V and define a function f:V→{−1,1}. The function f is a signed dominating function if for every vertex x∈V, the closed neighborhood of x contains more vertices with function value 1 than with −1. The signed domination number of G, γs(G), is the minimum weight of a signed dominating function on G. Let G denote the complement of G. In this paper we establish upper and lower bounds on γs(G)+γs(G).