Real and integer domination in graphs Original Research Article

For an arbitrary subset P of the reals, we define a function f: V → P to be a P-dominating function of graph G = (V,E) if the sum of the function values over any closed neighbourhood is at least 1. That is, for every ν ϵ V, |(N(ν) ∪{ν}) ⩾ 1. The P-domination numver of a graph is defined to be the infimum of |(V) taken over all P-dominating functions |. When P = {0, 1} one obtains the standard domination number. We obtain various theoretical and computational results on the P-domination number of a graph.