2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64443The k-th power D^k of a directed graph D is defined to be the directed graph on the vertices of D with an arc from a to b in D^k iff one can get from a to b in D with exactly k steps. This notion is equivalent to the k-fold composition of binary relations or k-th powers of Boolean matrices. A k-th root of a directed graph D is another directed graph R with R^k = D. We show that for each k >= 2, computing a k-th root of a directed graph is at least as hard as the graph isomorphism problem.15 pages, 4 figuresCombinatorics05C12, 05C20, 05C60 (Primary) 68Q17, 05C50, 15A23, 06E99 (Secondary)text