The signed and minus k-subdomination numbers of certain complete multipartite graphs and their complements

Abstract

Let G = (V, E) be a graph. For any real valued function f : V → R and S ⊆ V, let f(S) = ∑_υ∈s f(u). The weight of f is defined as f(V). A signed k-subdominating function (kSF) of G is defined as a function f : V → {-1, 1} such that f(N[υ]) ≥ 1 for at least k vertices of G. The signed k-subdomination number of a graph G, denoted by γ^-11_ks(G), is equal to min{f(V) | f is a signed kSF of G}. A minus kSF and the corresponding parameter, the minus k-subdomination number of G, denoted by γ^-101_ks(G), are defined similarly, except that 0 is now also an allowable value. In this paper we compute the minus and signed k-subdomination numbers for certain complete multipartite graphs and their complements.