The design of large-scale equipment manufacturing systems plays a crucial role in ensuring product performance, optimizing production efficiency, and reducing lifecycle costs. Effective reuse of domain knowledge is essential for maintaining both the quality and efficiency of manufacturing system design. Although existing knowledge graph technologies standardize the representation and storage of such domain knowledge, the complex design constraints and multiple optimization objectives of manufacturing systems still pose significant challenges to the efficient reuse of domain knowledge. Recent advancements in the large language model (LLM) and retrieval-augmented generation (RAG) have led to the emergence of graph retrieval-augmented generation (GraphRAG), which presents a promising approach to overcoming these challenges. This paper proposes a novel GraphRAG-based method, Design-on-Graph, to support knowledge management and automated generation of design plans for manufacturing systems. This method employs the LLM to intelligently retrieve and verbalize structured domain knowledge through multi-turn conversations, achieving high-efficiency knowledge management for manufacturing systems. Additionally, the retrieved domain knowledge is systematically archived within conversation history, providing contextual support for LLM-driven reasoning tasks to streamline automated design processes. Finally, a case study on an aircraft fuselage joint system is conducted, and an AI agent incorporating all the above functionalities is developed to demonstrate and evaluate the performance of the proposed Design-on-Graph.