Inspired by spatial traversal point cloud expression, we propose a serialization strategy based on graph point cloud representation, employing Depth First Search (DFS) and Breadth First Search (BFS). It includes ordered representations reliant on LiDAR scanning principles and graph representations according to sensor fields of view. DFS and BFS serialization organizes the global point cloud along geodesic edges in depth and breadth dimensions, preserving substantial geodesic information compared to traditional spatial traversal. On the vanilla SOTA Point Transformer backbone PTv3, the combined DFS and BFS encoding achieves the baseline semantic segmentation accuracy, with a mixed serialization strategy yielding a 1% improvement in performance. Furthermore, recognizing the disparities between NLP and point cloud serialization, we propose evaluation criteria for spatial semantics, continuity ambiguity, and differences in point cloud “words” known as patches to better analyze existing serialization patterns. DFS, with its enriched geodesic information, presents capabilities for expressing local structures akin to the Z-order and Hilbert serialization, while BFS offers unique advantages in local receptive field size, continuity ambiguity, and inter-patch differentiation.