Lower bounds on the signed k-domination number of graphs

Let G be a graph with vertex set V(G). For any integer k >= 1, a signed k-dominating function is a function f : V(G) -> {-1, 1} satisfying Sigma(x is an element of N[v]) f (x) >= k for every v is an element of V(G), where N[v] is the closed neighborhood of v. The minimum of the values Sigma(v is an element of V)(c) f(v), taken over all signed k-dominating functions f, is called the signed k-domination number. In this note we present some new lower bounds on the signed k-domination number of a graph. Some of our results improve known bounds.