Lower bounds on the signed total k-domination number of graphs

Let G be a graph with vertex set V(G). For any integer k a parts per thousand yen 1, a signed total k-dominating function is a function f: V(G) -> {-1, 1} satisfying a (xaN(v)) f(x) a parts per thousand yen k for every v a V(G), where N(v) is the neighborhood of v. The minimum of the values a (vaV(G)) f(v), taken over all signed total k-dominating functions f, is called the signed total k-domination number. In this note we present some new sharp lower bounds on the signed total k-domination number of a graph. Some of our results improve known bounds.