ABSTRACT
In Chapter 1 the concept of a dominating set and the domination number 'Y( G) of a graph were introduced. Various bounds for 'Y( G) in terms of a variety of other graphical parameters were presented in Chapter 2. In this chapter we will discuss the close relationships that exist among dominating sets, independent sets and irredundant sets in graphs. One result of these relationships is an inequality chain of parameters that has become one of the major focal points of the study of domination in graphs. We begin by discussing hereditary and superhereditary properties of sets of vertices in graphs. Much of this discussion is taken from a 1995 paper by Cockayne, Hattingh, Hedetniemi, Hedetniemi, and McRae 1271].
