Minus k-subdomination in graphs II Original Research Article

Let G = (V,E) be a graph and k ϵ Z+ such that if1 ⩽ k ⩽¦V¦. A (ifk-(rmsubdominating)) function (if(kSF)) to ⋐−1,0,1⋑ is a function iff : V → ⋐−1,0,1⋑ such that the closed neighborhood sum (iff(N[v]) ≥ 1) for at least k vertices of G. The weight of a kSF f is f(V) = ∑vϵVf(v). The k-subdomination number to ⋐−1,0,1⋑ of a graph G, denoted by γks−101(G), equals the minimum weight of a kSF of G. In this paper we give a sharp lower bound for γks−101(G) for trees and calculate γks−101 for an arbitrary cycle.