The three standard products (the Cartesian, the direct and the strong product) of undirected graphs have been repeatedly studied, unique prime factor decomposition (PFD) is known and polynomial time algorithms have been established for determining the prime factors.
For directed graphs, unique PFD results with respect to the standard products are known. However, there is, until now, no known algorithm to compute the PFD of directed graphs with respect to the direct and the strong product in general.