In this paper we examined the relation between digraph folding of a given pair of digraphs and digraph folding of new digraphs generated from these given pair of digraphs by some known operations like union, intersection, join, Cartesian product and composition. We first redefined these known operations for digraphs, then we defined some new maps of these digraphs and we called these maps union, intersection, join, Cartesian and composition dimaps .In each case we obtained the necessary and sufficient conditions, if exist ,for a dimap to be digraph folding. Finally we explored the digraph folding, if there exist any, by using the adjacency matrices. Key words: Digraphs, adjacency matrices , digraph folding ,union,intersection, join, the Cartesian product and the composition of digraphs .