A Generalization of the Generalized Petersen Graphs and N2R Network Structures

Recently N2R network topologies, which are a subset of the Generalized Petersen Graphs - have been introduced as an alternative to Double Rings. They have been shown to be superior compared to double rings in terms of average distance, diameter and several other parameters. In this paper a further generalization is introduced, with two inner rings instead of just one. By having different jump lengths of these two inner rings it is shown that the distances are significantly reducedwhile the topologies are still 3-regular and 3-connected. It is a minor drawback that these new topologies are less symmetric, but we show that the distance parameters are quite similar regardless of which node in the network they are measured from