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

Abstract

We propose a new family of interconnection networks (WGnm) with regular degree three. When the generator set is chosen properly, they are isomorphic to Cayley graphs on the wreath product Zm ≀ Sn. 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.