Recursive cubes of rings as models for interconnection networks

TL;DR

This paper models recursive cubes of rings as Cayley graphs to analyze their properties, providing algorithms for shortest paths and exact diameters, and establishing bounds on key network parameters.

Contribution

It introduces an algebraic framework for recursive cubes of rings and derives exact and bounded measures for their network performance metrics.

Findings

Algorithm for shortest path computation

Exact diameter values obtained

Bounds established for Wiener index and forwarding indices

Abstract

We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths 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 the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks.