Abstract. If G is a graph, then its P_k-path graph, P_k(G), has vertex set identical with the set of paths of length k in G, with two vertices adjacent in P_k(G) if and only if the coresponding paths are "consecutive" in G.

By L(G) we denote a 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)).

We present algorithms, which allow us to compute independence numbers of P₂-path graphs and P₃-path graphs of special graphs. As P₂(G) and P₃(G) are subgraphs of iterated line graphs L²(G) and L³(G), respectively, we compare our results with the independence numbers of corresponding iterated line graphs.