Recursive cubes of rings as models for interconnection networks

摘要

We study recursive cubes of rings as models for interconnection networks. Wefirst redefine each of them as a Cayley graph on the semidirect product of anelementary abelian group by a cyclic group in order to facilitate the study ofthem by using algebraic tools. We give an algorithm for computing shortestpaths and the distance between any two vertices in recursive cubes of rings,and obtain the exact value of their diameters. We obtain sharp bounds on theWiener index, vertex-forwarding index, edge-forwarding index and bisectionwidth of recursive cubes of rings. The cube-connected cycles and cube-of-ringsare special recursive cubes of rings, and hence all results obtained in thepaper apply to these well-known networks.