Let  be a connected, simple and undirected graph. A subset D of V is -irredundant if for every x in D either    or there exists  such that   and maximum cardinality of a maximal -irredundant set of G are, respectively, called the -irredundance number and upper -irredundance number of G and are denoted by  and  respectively. In this paper, -irredundant sets in graph are introduced and studied. The aim of this paper is to study this new parameter.

(k, r)-irredundant sets, (k, r)-dominating sets.