The (ℝ,d,d',ℝ-1)-problem is that of finding large graphs with maximum degree ℝ and diameter d such that the subgraphs obtained by deleting any set of up to ℝ-1 vertices have diameter ¸•d'. In this paper, the authors deduce upper bounds on the order of such graphs and present some of the largest known ones. They argue that these graphs can be used to construct extremely ‘robust’ networks, and explain why this robustness property is required when designing transputer networks for certain applications. In particular, the authors investigate the suitability of the odd graph O4 as a topology for such networks.
