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

Abstract

Let G be a graph with vertex set V(G). For any integer k ≥ 1, a signed total k-dominating function is a function f: V(G) → {−1, 1} satisfying ∑ _x∈N(v) f(x) ≥ k for every v ∈ V(G), where N(v) is the neighborhood of v. The minimum of the values ∑ _v∈V(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.