EXTREMUM AGGREGATES OF MINIMAL 0-DOMINATING FUNCTIONS OF GRAPHS
P.J.P. Grobler, Christina M. Mynhardt · Quaestiones Mathematicae · 1996
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) = ΣvεV 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.