A Survey on Chordal Rings, N2R and Other Related Topologies
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paper_title: Improving Topological Routing in N2R Networks

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Topological routing is basically table free, and allows for very fast restoration and thus a high level of reliability in communication. It has already been satisfactorily proposed for some regular structures such as Grid or Honeycomb. An initial proposal has also been developed for the N2R structures. This paper proposes a modification of this previous algorithm, and in addition two other alternatives. The three options are systematically analyzed in terms of executing time and path distances, showing that trade-offs are needed in order to determine which algorithm is best for a given case. Also, the possible practical applications the methods could have, are discussed for different traffic scenarios.
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paper_title: Self-dual configurations and regular graphs

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A rotary internal combustion engine including a plurality of segregated chambers arranged in communicating relation with one another such that compression, combustion and expansion of the gases used to rotate the engine may take place in succession, step-like manner. Each of the chambers have mounted therein a rotary pump which may be in the form of a pair of multi-lobed intermeshing rotors mounted on two parallel drive shafts. Alternately, the rotary pumps may be in the form of a single rotor mounted on a single drive shaft which extends through each of the successively arranged chambers so as to position the rotor in movable working relation with the interior of the cylinder.
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paper_title: Traffic load on interconnection lines of generalized double ring network structures

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Generalized double ring (N2R) network structures possess a number of good properties, but being not planar they are hard to physically embed in communication networks. However, if some of the lines, the interconnection lines, are implemented by wireless technologies, the remaining structure consists of two planar rings, which are easily embedded by fiber or other wired solutions. It is shown that for large N2R structures, the interconnection lines carry notably lower loads than the other lines if shortest-path routing is used, and the effects of two other routing schemes are explored, leading to lower load on interconnection lines at the price of larger efficient average distance and diameter
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paper_title: Five Novel Selection Policies for N2R Network Structures

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This paper shows how 5 new selection policies can be applied to N2R structures. For each number of nodes, a selection policy determines which topology is chosen. Compared to approaches taken previously, the policies proposed in this paper allow us to choose structures which are significantly easier to implement, while having only slightly longer distances. The 5 policies reflect different trade-offs between distances and ease of implementation, and two of them explore the potentials of using N2R(p; q; r) instead of N2R(p; q) structures.
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paper_title: Describing N2R Properties Using Ideal Graphs

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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.
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paper_title: Using Different Chord Lengths in Degree Three Chordal Rings and N2R Topologies

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Degree Three Chordal Rings and N2R Topologies are useful for physial and optical network topologies due to the combination of short dis- tances, regularity and low degrees. In this paper we show how distances in terms of average distances and diameters can be significantly decreased by us- ing chords of different lengths. These topologies are slightly less symmetric than the traditional ones, but the distances are virtually the same no matter which node in a given topology they are measured from.
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Title: A Survey on Chordal Rings, N2R and Other Related Topologies

Section 1: Introduction
Description 1: Describe the significance and the increasing dependence of society on communication infrastructures, and provide an overview of the role of network topologies in ensuring connectivity, reliability, and quality.

Section 2: Basic notation and definitions
Description 2: Define the basic terms and parameters used in network topologies, such as graphs, nodes, edges, path length, distance, and node degree, along with metrics for evaluating topologies.

Section 3: N2R
Description 3: Discuss the Network of 2 Rings (N2R) topology, its structure, properties, and various studies about its distances, traffic distribution, routing schemes, and reliability.

Section 4: Chordal Rings
Description 4: Explain the chordal ring topology, including its definition, structure with chords, and degree, and summarize related studies on distances, routing, and comparative analysis with N2R.

Section 5: Further works
Description 5: Highlight collaborative efforts between the two universities on extending the work on CR and N2R topologies, proposing new variants, analyzing their characteristics, and studying their reliability and routing mechanisms.

Section 6: Conclusion and outlook
Description 6: Provide a summary of the key findings from the survey, and discuss the potential future directions in the study and implementation of these network topologies.