Changing and unchanging of the domination number of a graph

Let G be a graph and @c(G) denote the domination number of G. A dominating set D of a graph G with |D|[email protected](G) is called a @c-set of G. A vertex x of a graph G is called: (i) @c-fixed if x belongs to every @c-set, (ii) @c-free if x belongs to some @c-set but not to all @c-sets, (iii) @c-bad if x belongs to no @c-set, (iv) @c^--free if x is @c-free and @c(G-x)[email protected](G)-1, (v) @c^0-free if x is @c-free and @c(G-x)[email protected](G), and (vi) @c^q-fixed if x is @c-fixed and @c(G-x)[email protected](G)+q. In this paper we investigate for any vertex x of a graph G whether x is @c^q-fixed, @c^0-free, @c^--free or @c-bad when G is modified by deleting a vertex or adding or deleting an edge.