A new view on the DEDS control synthesis is presented. Petri nets (PN), frequently used for DEDS modelling, are understood here in a form of a corresponding oriented graphs (OG) where the nodes of the OG are represented by the PN positions and the OG edges involve the PN transitions. The adjacency matrix of such a graph is utilized in the DEDS control synthesis procedure. It is used for generating the state reachability tree in both the case of the straight-lined system development (from an initial state to a prescribed terminal one) and that of the backtracking one (from the prescribed terminal state to the initial one). A suitable combination of both the straight-lined development of the OG-based model and the backtracking one is used in this paper in order to perform the DEDS control synthesis. The coincidence both of the corresponding trees yields the possible trajectories of the system development. Satisfying sequences of the control discrete events are found by means of the OG adjacency matrix.