2017/03/09 by Ghameshlou, Arezoo N.
#05C69 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1703.03268
Let 1 ≤ k ≤ n be a positive integer. A \em nonnegative signed k-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 \em nonnegative signed k-subdomination number of G and denoted by γNNks(G). When k=|V(G)|, γNNks(G)=γNNs(G) is the \em nonnegative signed domination number, introduced in \citeHLFZ. In this paper, we investigate several sharp lower bounds of γNNs(G), which extend some presented lower bounds on γNNs(G). We also initiate the study of the nonnegative signed k-subdomination number in graphs and establish some sharp lower bounds for γNNks(G) in terms of order and the degree sequence of a graph G.