Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are widely used project management tools for scheduling and controlling complex projects. However, solving CPM and PERT problems can be computationally intensive and time-consuming, especially for large-scale projects. This paper presents a novel approach to solving CPM and PERT problems using graph theory in Java. We represent project networks as directed graphs and apply graph algorithms to identify critical paths, calculate earliest start and finish times, and determine slack times. Our Java implementation utilizes efficient graph traversal techniques and data structures to optimize performance. Experimental results demonstrate the effectiveness and efficiency of our approach, showing significant improvements in computation time and scalability compared to traditional methods. This research contributes to the development of more efficient project management tools and provides a foundation for further research in applying graph theory to project scheduling problems.