A new family of interconnection networks of odd fixed degrees ?
We propose a new family of interconnection networks WG n m that are Cayley graphs with fixed degrees of any odd number greater than or equal to three. When the generator set is chosen properly, they are isomorphic to Cayley graphs  of the wreath product Zm?Sn Z m ? S n . In the case of m?3 m ? 3 and n?3 n ? 3 , we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by 9 8 n 2 - 1 4 n + 2 . Some embedding properties are also derived. Finally, we compare the proposed networks with some popular topologies.
interconnection network cayley graph routing diameter embedding