Abstract. If G is a graph, then its path graph, Pk(G), has vertex set identical with the set of paths of length k in G, with two vertices adjacent in Pk(G) if and only if the corresponding paths are "consecutive" in G. By diam(G) we denote the diameter of G. We study the behaviour of diam(P2i(G)) as a function of i, where P2i(G) is a composition P2(P2i-1(G)), with P20(G))=G.
Let G be a graph. Then P2i(G) may contain plenty of isolated vertices and at most one nontrivial component. Let us denote this component by Hi. Belan and Jurica proved
We remark that the situation is analogous for line graphs and iterated line graphs. We have