A P-Graph is defined to be structurally feasible or to be a solution-structure of synthesis problem if it satisfies the following axioms.

(S1) Every final product is represented in the graph.

(S2) A vertex of the M-type has no input if and only if it represents a raw material.

(S3) Every vertex of the O-type represents an operating unit defined in the synthesis problem.

(S4) Every vertex of the O-type has at least one path leading to a vertex of the M-type representing a final product.

(S5) If a vertex of the M-type belongs to the graph, it must be an input to or output from at least one vertex of the O-type in the graph.

Axiom (S1) implies that each product is produced by at least one of the operating units of the system; axiom (S2), a material is not produced by any operating unit of the system if and only if this material is a raw material; axiom (S3), only the plausible operating units of the problem are taken into account in the synthesis; axiom (S4), any operating unit of the system has a series of connections eventually leading to the operating unit generating at least one of the products; and axiom (S5), each material appearing in the system is an input to or an output from at least one operating unit of the system.