We propose to design vertex encoding for determinations of no-result edge queries that should not be executed. Edge query is one of the core operations in mainstream graph databases, which is to retrieve edges connecting two given vertices. Real-world graphs may be too large to be stored in memory and frequently accessing edge data on disk usually incurs much overhead. The average degree of real-world graph tends to be much less than the vertex number, and edges may not exist in most pairs of vertices. Efficiently avoiding no-result edge query executions will certainly improve the performance of graph database. In this article, we propose a new and important problem for determining no-result edge queries: vertex encoding for edge nonexistence determination (VEND, for short). We build a low dimensional vertex encoding for all vertices, and we can efficiently determine most vertex pairs that are connected by no edges just with their corresponding codes. The encoding can be efficiently adjusted when data updates happen. With VEND, we can utilize in-memory efficient operations to filter no-result disk accesses for edge query. We also design SIMD-oriented compression optimizations to further improve performance. Extensive experiments on real-world datasets confirm the effectiveness of our solution.