EXTREMUM AGGREGATES OF MINIMAL 0-DOMINATING FUNCTIONS OF GRAPHS

Abstract

A 0-dominating function 0DF of a graph G = (V,E) is a function f: V → [0,1] such that Σ _xεN(v) f(x) ≥ 1 for each ν ε V with f(v) = 0. The aggregate of a 0DF f is defined by ag(f) = Σ_vεV f(v) and the infimum and supremum of the set of aggregates over all minimal 0DFs of a graph are denoted by γ₀ and Γ₀ respectively. We prove some properties of minimal 0DFs and determine γ₀ and Γ₀ for some classes of graphs.