Manufacturing Process Selection (MPS) plays a critical role in ensuring product quality, cost efficiency, and sustainability. A great deal of knowledge and experience is needed to determine the most appropriate set of manufacturing processes to realize a product. Thus, effectively capturing, organizing, and utilizing related knowledge is essential. Traditional MPS methods rely on pre-determined criteria and frameworks, limiting their adaptability to new knowledge and flexible process selection needs. To address this limitation, we propose an adaptive MPS framework that integrates Knowledge Graphs (KG) with manufacturing processes knowledge, along with MPS rules to enable explainable and flexible process selection. The framework retrieves relevant knowledge from KGs and applies decision rules to guide the execution of MPS tasks without the need for human expert intervention. It includes an automated knowledge extraction and integration module leveraging Large Language Models to ensure continuous updates to manufacturing knowledge. The proposed framework was validated using a case study, integrating a new manufacturing process into the KGs and identifying the optimal manufacturing processes for a respirator mask facepiece. This study demonstrates the feasibility of using graph topology-based knowledge and decision rules for adaptive and automated MPS tasks. Future work will focus on expanding the KG scheme with more types of MPS knowledge and rules and improving knowledge extraction and integration techniques for broader industrial applications.