A New Family of Trivalent Cayley Networks on Wreath Product Z m ≀ S n

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 ⌈m/2⌉ (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.