Inequalities involving independence domination, f-domination, connected and total f-domination numbers

Let f be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an f-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an f-dominating set is defined to be the f-domination number, denoted by rf(G) In a similar way one can define the connected and total f-domination numbers gamma(c,f)(G) and gamma(t,f)(G) If f(x) = 1 for all vertices x, then these are the ordinary domination number, connected domination number and total domination number of G, respectively. In this paper we prove some inequalities involving gamma(f)(G),gamma(c),(f)(G),gamma(t),(f)(G) and the independence domination number i(G). In particular, several known results are generalized.