Virtual network mapping (VNM) is a challenge in the field of network virtualization. As VNM variants have been formalized depending on substrate network structures, virtual network specifications, mapping optimization objectives, and other factors, a number of VNM heuristic methods have been introduced. On the other hand, reinforcement learning (RL) algorithms have been incorporated into deep learning frameworks and recognized as a promising solution for solving complex resource allocation problems. In this paper, we present an RL-based graph embedding and mapping framework, Gemma, for tackling various VNM problems in a unified end-to-end manner. In the framework, we employ an encoder-decoder deep learning architecture and propose several optimization schemes such as two-stage mapping and model-based selective embedding. Aiming to deal with large-scale VNM problems in both online and offline scheduling systems, the proposed schemes explore the trade-off between inference accuracy and mapping function runtimes, enhancing scalability and timeliness. Gemma shows robust performance under various problem conditions, outperforming other heuristic and learning-based methods.