Minimum fractional dominating functions and maximum fractional packing functions

The fractional analogues of domination and 2-packing in a graph form an interesting pair of dual linear programmes in that the feasible solutions for both are functions from the vertices of the graph to the unit interval; efficient (fractional) domination is accomplished when one function simultaneously solves both LPs. We investigate some structural properties of the functions thus defined and classify some families of graphs according to how and whether the sets of functions intersect, developing tools that have proven useful in approaching problems in domination theory.