Abstract
The (Δ,d, d′, Δ − 1)-problem is that of finding large graphs with maximum degree Δ and diameterd such that the subgraphs obtained by deleting any set of up to Δ − 1 vertices have diameter≤d′. In this paper, we deduce upper bounds on the order of such graphs and present some of the largest known ones. We argue that these graphs can be used to construct extremely "robust" networks, and explain why we require this robustness property when designing transputer networks for certain applications. In particular, we investigate the suitability of the odd graphO 4 as a topology for such networks.
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Yebra, J.L.A., Rayward-Smith, V.J. & Revitt, A.P. The (Δ,d, d′, Δ − 1)-problem with applications to computer networks. Ann Oper Res 33, 113–124 (1991). https://doi.org/10.1007/BF02073596
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DOI: https://doi.org/10.1007/BF02073596