We present a novel graph Transformer generative adversarial network (GTGAN) to learn effective graph node relations in an end-to-end fashion for the challenging graph-constrained house generation task. The proposed graph-Transformer-based generator includes a novel graph Transformer encoder that combines graph convolutions and self-attentions in a Transformer to model both local and global interactions across connected and non-connected graph nodes. Specifically, the proposed connected node attention (CNA) and non-connected node attention (NNA) aim to capture the global relations across connected nodes and non-connected nodes in the input graph, respectively. The proposed graph modeling block (GMB) aims to exploit local vertex interactions based on a house layout topology. Moreover, we propose a new node classification-based discriminator to preserve the high-level semantic and discriminative node features for different house components. Finally, we propose a novel graph-based cycle-consistency loss that aims at maintaining the relative spatial relationships between ground truth and predicted graphs. Experiments on two challenging graph-constrained house generation tasks (i.e., house layout and roof generation) with two public datasets demonstrate the effectiveness of GTGAN in terms of objective quantitative scores and subjective visual realism. New state-of-the-art results are established by large margins on both tasks.