Graph edit distance (GED) is a fundamental measure for graph similarity analysis in many real applications. GED computation has known to be NP-hard and many heuristic methods are proposed. GED has two inherent characteristics: multiple optimum node matchings and one-to-one node matching constraints. However, these two characteristics have not been well considered in the existing learning-based methods, which leads to suboptimal models. In this paper, we propose a novel GED-specific loss function that simultaneously encodes the two characteristics. First, we propose an optimal partial node matching-based regularizer to encode multiple optimum node matchings. Second, we propose a plane intersection-based regularizer to impose the one-to-one constraints for the encoded node matchings. We use the graph neural network on the association graph of the two input graphs to learn the cross-graph representation. Our experiments show that our method is 4.2x-103.8x more accurate than the state-of-the-art methods on real-world benchmark graphs.