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

Abstract

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 cursive Greek chi outside D is adjacent to at least f (cursive Greek chi) vertices in D. The minimum number of vertices in an f-dominating set is defined to be the f-domination number, denoted by γf (G). In a similar way one can define the connected and total f-domination numbers γc, f (G) and γt, f (G). If f (cursive Greek chi) = 1 for all vertices cursive Greek chi, 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 γf (G), γt, f (..