Abstract
The wide diameter of a graph is an important parameter to measure fault-tolerance of interconnection network. This paper proves that for any two vertices in de Bruijn undirected graph UB(d,n), there are 2d−2 internally disjoint paths of length at most 2n+1. Therefore, the (2d−2)-wide diameter of UB(d,n) is not greater than 2n+1.
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Dedicated to Professor Frank K. Hwang on the occasion of his sixty fifth birthday.
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Kuo, J., Fu, HL. Wide diameters of de Bruijn graphs. J Comb Optim 14, 143–152 (2007). https://doi.org/10.1007/s10878-007-9066-4
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DOI: https://doi.org/10.1007/s10878-007-9066-4