On Minus Paired－Domination in Graphs

The study of minus paired-domination of a graph G = ( V, E) is initiated. Let S lontain in V be any paired-dominating set of G, a minus paired-dominating function is a function of the form f: V→ { - 1, 0, ｝such that f(υ) = 1 for υ∈S, f(υ)≤0 for υ∈V- S, and f(Nυ])≥l for all υ∈V. The weight of a minus paired-dominating function f is ω(f)=∑f(υ), over all vertices υ∈V. The minus paired-domination number of a graph G is γp^-(G)= min｛ω (f)| f is a minus paired-dominating function of G｝. On the basis of the minus paired-domination number of a graph G defined, some of its properties are discussed.

On Minus Paired-Domination in Graphs

The study of minus paired-domination of a graph G=(V,E) is initiated. Let SV be any paired-dominating set of G, a minus paired-dominating function is a function of the form f∶V→{-1,0,1} such that f(v)=1 for v∈S, f(v)≤0 for v∈V-S, and f(Nv])≥1 for all v∈V. The weight of a minus paired-dominating function f is w(f)=∑f(v), over all vertices v∈V. The minus paired-domination number of a graph G is γ-p(G)=min{w(f)|f is a minus paired-dominating function of G}. On the basis of the minus paired-domination number of a graph G defined, some of its properties are discussed.