This paper addresses the limitations of existing fully connected graph representations in generalized planning, combining reinforcement learning (RL) and graph neural networks (GNNs), in various symbolic planning domains described by PDDL. Existing methods represent planning states as fully connected graphs, which can lead to combinatorial explosion and sparsity problems as the problem size increases, especially in large grid-based environments. These dense representations dilute node-level information and exponentially increase memory requirements, making learning on large-scale problems impossible. In this paper, we propose a sparse, goal-aware GNN representation that selectively encodes relevant local relationships and explicitly incorporates objective-related spatial features. We validate the proposed method by designing novel PDDL-based drone mission scenarios within a grid world. Experimental results demonstrate that the proposed method effectively scales to larger grid sizes, which is not possible with existing dense graph representations, and significantly improves policy generalization and success rates.