Describing N2R Properties Using Ideal Graphs

Abstract

N2R structures are a subset of Generalized Petersen Graphs and a potentially good option to be used for implementing degree three networks. The previous works on these structures verify that N2R are better than other degree three regular topologies such as Double Rings or Honeycomb in terms of path distances. The cost of this good performance is a more complex and non-planar interconnection configuration; It is complex to find analytical models to be used, for example for describing topological parameters. This paper proposes and verifies the possibility of approximating real N2R graphs to optimal and ideal graphs, which are much easier to model, obtaining fairly accurate results. A main result of the paper is a simple formula for approximating average distance and diameter given the number of nodes in a N2R graph.