Abstract: ‍ ‍In this paper， multichannel speech enhancement in the graph frequency domain is investigated， and a joint graph topology in the spatial-temporal dimension is constructed using graph signal processing （GSP） theory， based on which enhancement algorithms are designed for multichannel speech denoising. Specifically， a temporal graph topology is constructed based on the temporal correlation of speech vertex signals between the input frames of a microphone of the input array； Meanwhile， a spatial graph topology based on the spatial correlation of received signals in each channel is built for multi-channel noisy speech. Based on a joint graph topology composed of temporal and spatial bipartite graph topologies， a joint graph topology-based minimum variance distortionless response （MVDR） enhancement algorithm in the graph frequency domain is used to perform multichannel speech enhancement. Numerical simulation results show that the proposed joint graph topology-based MVDR （JG-MVDR） beamforming method outperforms both the regular graph-based MVDR （GMVDR） beamforming method and the complex Gaussian mixture model based MVDR （CGMM-MVDR） beamforming method in terms of the average perceptual evaluation of speech quality （PESQ） and the average extended short-time objective intelligibility （ESTOI）.