With the development of 5G technologies and the wide application of artificial intelligence (AI), the mobile intelligent equipment and the providing services have both seen a significant rise in numbers and types. Some services, such as vehicular tasks, may go beyond the capability of the mobile equipment so that task offloading is required to help deliver such services. However, the graph structure of task offloading data, which can be a key to further improve algorithm's performance, is seldomly considered in future 6G-AI combined communication systems. In this article, we propose an efficient end-edge-cloud orchestration system that combines storage-partition and computation-shared in cloud cluster, cache mechanism, and cybertwin components. At the same time, we model this dynamic system as a graph structure composed of nodes and edges and propose a novel task offloading algorithm that incorporates a graph attention network (GAT) and action branching into deep deterministic policy gradient (DDPG) framework. Numerical results show that our offloading scheme achieves a good performance boost compared with other baseline schemes.