PURPOSE: Deformable image registration (DIR) plays an important role in assisting disease diagnosis. The emergence of the Transformer enables the DIR framework to extract long-range dependencies, which relieves the limitations of intrinsic locality caused by convolution operation. However, suffering from the interference of missing or spurious connections, it is a challenging task for Transformer-based methods to capture the high-quality long-range dependencies.METHODS: In this paper, by staking the graph convolution Transformer (Graformer) layer at the bottom of the feature extraction network, we propose a Graformer-based DIR framework, named GraformerDIR. The Graformer layer is consist of the Graformer module and the Cheby-shev graph convolution module. Among them, the Graformer module is designed to capture high-quality long-range dependencies. Cheby-shev graph convolution module is employed to further enlarge the receptive field.RESULTS: The performance and generalizability of GraformerDIR have been evaluated on publicly available brain datasets including the OASIS, LPBA40, and MGH10 datasets. Compared with VoxelMorph, the GraformerDIR has obtained performance improvements of 4.6% in Dice similarity coefficient (DSC) and 0.055 mm in the average symmetric surface distance (ASD) while reducing the non-positive rate of Jacobin determinant (Npr.Jac) index about 60 times on publicly available OASIS dataset. On unseen dataset MGH10, the GraformerDIR has obtained the performance improvements of 4.1% in DSC and 0.084 mm in ASD compared with VoxelMorph, which demonstrates the GraformerDIR with better generalizability. The promising performance on the clinical cardiac dataset ACDC indicates the GraformerDIR is practicable.CONCLUSION: With the advantage of Transformer and graph convolution, the GraformerDIR has obtained comparable performance with the state-of-the-art method VoxelMorph. <<<