A graph-theoretic method for integration of process and control system (IPCS) syntheses with different controllability notions has been proposed in the present paper. The foundation of this integration is a well-established, graph-theoretic approach to process synthesis in conjunction with the analysis of structural controllability based on digraph-type process models. Unambiguous structural representation of the resultant integrated process and control systems, IPXS structures in brief, has been introduced for unambiguous representation of a process structure, it is rendered possible as an extension of the directed bipartite graph, the P-graph. Different set of axioms are proposed for describing the case of disturbance-rejective regulable and the combinatorially feasible and controllable structures in the special cases considered : the case of structural controllability and the case of fault-tolerant controllability. These axioms make the synthesis computationally more effective by considering very simple engineering knowledge. The maximal controllable structure of an IPXS synthesis problem has been defined as the union of combinatorially feasible and controllable IPXS structures. Thus, the mathematical programming model, e.g. MINLP model, of an IPXS synthesis problem can be and should be derived from the maximal controllable structure. Different versions of a fundamental polynomial time, combinatorial algorithm are presented for identifying the maximal controllable structure. The resultant IPXS structures are compared with the structures synthesized without considering their control systems.