The axial field of view (FOV) is a key factor that affects the quality of PET images. Due to hardware FOV restrictions, conventional short-axis PET scanners with FOVs of 20 to 35 cm can acquire only low-quality PET (LQ-PET) images in fast scanning times (2-3 minutes). To overcome hardware restrictions and improve PET image quality for better clinical diagnoses, several deep learning-based algorithms have been proposed. However, these approaches use simple convolution layers with residual learning and local attention, which insufficiently extract and fuse long-range contextual information. To this end, we propose a novel two-branch network architecture with swin transformer units and graph convolution operation, namely SW-GCN. The proposed SW-GCN provides additional spatial- and channel-wise flexibility to handle different types of input information flow. Specifically, considering the high computational cost of calculating self-attention weights in full-size PET images, in our designed spatial adaptive branch, we take the self-attention mechanism within each local partition window and introduce global information interactions between nonoverlapping windows by shifting operations to prevent the aforementioned problem. In addition, the convolutional network structure considers the information in each channel equally during the feature extraction process. In our designed channel adaptive branch, we use a Watts Strogatz topology structure to connect each feature map to only its most relevant features in each graph convolutional layer, substantially reducing information redundancy. Moreover, ensemble learning is adopted in our SW-GCN for mapping distinct features from the two well-designed branches to the enhanced PET images. We carried out extensive experiments on three single-bed position scans for 386 patients. The test results demonstrate that our proposed SW-GCN approach outperforms state-of-the-art methods in both quantitative and qualitative evaluations.