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Relationships among popular interconnection Networks
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Star generated graphs were proposed as an attractive alternative to hypercubes for massive parallel computing in early 1980s, due to sublogarithmic regularity and diameter. However, star graphs suffer from n! vertices. As the gaps between (n-1)! and n! grow too fast to be considered for practical implementation. (n,k)-Arrangement graphs and (n,k)-Star graphs were proposed as a remedy for n! problem. Star graphs are one extreme case in a general class of Cayley graphs generated by transposition trees. This work generalizes Cayley graphs generated by transposition trees to a class that contains both (n,k)-Arrangement graphs and (n,k)-Star graphs as special cases. Moreover connectivity properties, decomposition methods, relationships among different classes of interconnection networks and local orientation rules are derived. Finally, even more general and flexible class of interconnection networks is introduced.
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