Automated ICD coding involves assigning standardized diagnostic codes to clinical narratives. The vast label space and extreme class imbalance continue to challenge precise prediction. To address these issues, LabGraph is introduced -- a unified framework that reformulates ICD coding as a graph generation task. By combining adversarial domain adaptation, graph-based reinforcement learning, and perturbation regularization, LabGraph effectively enhances model robustness and generalization. In addition, a label graph discriminator dynamically evaluates each generated code, providing adaptive reward feedback during training. Experiments on benchmark datasets demonstrate that LabGraph consistently outperforms previous approaches on micro-F1, micro-AUC, and P@K.