Lower bounds on nonnegative signed domination parameters in graphs

Abstract

Let 1≤k≤n be a positive integer. A nonnegative signedk-subdominating function is a function f:V(G)→{−1,1} satisfying ∑u∈NG[v]f(u)≥0 for at least k vertices v of G. The value min∑v∈V(G)f(v), taking over all nonnegative signed k-subdominating functions f of G, is called the nonnegative signedk-subdomination number of G and denoted by γksNN(G). If k=|V(G)|, then γksNN(G)=γsNN(G) is the nonnegative signed domination number, introduced in Huang et al. (2013) . In this paper, we obtain several sharp lower bounds of γsNN(G), which extend some known lower bounds on γsNN(G).We also initiate a study of the nonnegative signed k-subdomination number in graphs and establish some sharp lower bounds for γksNN(G) in terms of the order and the degree sequence of a graph G.