Abstract
We propose a new family of interconnection networks (WG n m) with regular degree three. When the generator set is chosen properly, they are isomorphic to Cayley graphs on the wreath product Z m ≀ S n . In the case of m ≥ 3 and n ≥ 3, we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by \(\lceil\frac{m}{2}\rceil (3n^2-8n+4)-2n+1\). The connectivity and the optimal fault tolerance of the proposed networks are also derived. In conclusion, we present comparisons of some familiar networks with constant degree 3.
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This work was partly supported by the Natural Science Foundation of Fujian Education Ministry under Grant No. JB05333.
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Zhou, S. A New Family of Trivalent Cayley Networks on Wreath Product Z m ≀S n . Jrl Syst Sci & Complex 19, 577–585 (2006). https://doi.org/10.1007/s11424-006-0577-3
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DOI: https://doi.org/10.1007/s11424-006-0577-3