Lower Bounds on the Signed \(k\)-Subdomination Number of Graphs

Abstract

Let \(G = (V,E)\) be a simple graph. For any real valued function \(f:V \to {R}\) and \(S \subset V\), let \(f(S) = \sum_{v\in S} f(u)\). A signed \(k\)-subdominating function is a function \(f: V \to \{-1,1\}\) such that \(f(N[v]) \geq 1\) for at least \(k\) vertices \(v \in V\). The signed \(k\)-subdomination number of a graph \(G\) is \(\gamma_{ks}^{-11}(G) = \min \{f(V) | f \text{ is a signed } k\text{-subdominating function on } G\}\). In this paper, we obtain lower bounds on this parameter and extend some results in other papers.