Abstract. By L(G) we denote the line graph of G. We set L⁰(G)=G. For i>0 the i-iterated line graph of G is Lⁱ(G)=L(L^i-1(G)).

Let k>0 be an integer and let G=(V(G),E(G)) be a graph. A set S of vertices of G is k-independent if the distance between any two vertices of S is at least k+1. We denote by R_k(G) the maximum cardinality among all k-independent sets of G. Number R_k(G) is the k-packing number of G. Furthermore, S is k-dominating set if every vertex in V(G)-S is at distance at most k from some vertex in S. A set S is k-independent dominating if it is both k-independent and k-dominating . The k-independent dominating number, i_k(G), is the minimum cardinality among all k-independent dominating sets of G.

In the paper we find the values i_k(G) and R_k(G) for iterated line graphs. Our results show that if G is a regular graph, then we can immediately write the numbers i_k(Lⁱ(G)) and R_k(Lⁱ(G)) if i is bigger than k+c, where c is a constant which dsoes not depend on G.