Diameter in iterated path graphs

Abstract If G is a graph, then its 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 corresponding paths are ‘consecutive’ in G . We study the behavior of diam (P 2 i (G)) as a function of i , where P 2 i (G) is a composition P 2 (P 2 i−1 (G)) , with P 2 0 (G)=G .