Petri nets concepts provide additional tool for the modeling of metabolic networks. Especially the concepts of siphon and trap are used to study the role of trios phosphate isomerase’s (TPI) in trypanosome brucei metabolism. In this paper we show that the marked graph for groups with generating set has subset of places whose input transitions is equal to the output transitions and both of them equal to the set of all transitions of the marked graph if the group is (D2n , A) and hence that the dual of this Marked graph can be associated with a Phosphorus cycle.