ABSTRACT
For various properties P related to domination and a given graph G = {V, E), the class of vertex subsets of G having property P have been embedded in some set F p of real valued functions defined on V For example, the dominating sets of G have been embedded in the set of dominating functions of G. This work surveys results about the convexity of the set of extremal elements of F p when P is domination, total domination and packing. In each case most of the results concern the existence of universal extremal elements of F p Some of these results are special cases of more general theorems in a unifying theory, that of η functions.
