The signed and minus k-subdomination numbers of comets

Abstract Let G = (V,E) be a graph. For any real valued function f : V → R and S ⊆ V , let f(S) − ∑uϵs 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 → [t-1,1] such that f(N[v]) ≥ 1 for at least k vertices of G. The signed k-subdomination number of a graph G, denoted by γks−11(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 γks−101(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 a class of trees called comets.