A method for performing graph convolutions based on block Krylov subspace forms has been proposed. Two novel GCN architectures (a denseNet-like architecture and stacks truncated Krylov blocks) that make use of the multi-scale information in different ways have been proposed and analysed. The proposed architectures have been evaluated and compared to 3 common datasets (all for classification of scientific publications into one of several classes), and the results are fairly convincing. There is a clear consensus among the reviewers for acceptance. Hence, we recommend acceptance.