Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Optimal Distance Networks of Low Degree for Parallel Computers
IEEE Transactions on Computers
Computing the diameter in multiple-loop networks
Journal of Algorithms
On the k-diameter of k-regular k-connected graphs
Discrete Mathematics
A´da´m's conjecture is true in the square-free case
Journal of Combinatorial Theory Series A
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
Optimal Layouts of Midimew Networks
IEEE Transactions on Parallel and Distributed Systems
A Combinatorial Problem Related to Multimodule Memory Organizations
Journal of the ACM (JACM)
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
A survey on multi-loop networks
Theoretical Computer Science
On planarity and colorability of circulant graphs
Discrete Mathematics
An optimal message routing algorithm for circulant networks
Journal of Systems Architecture: the EUROMICRO Journal
Broadcasting in Optimal Bipartite Double Loop Graphs
IV '06 Proceedings of the conference on Information Visualization
Dense Gaussian networks: suitable topologies for on-chip multiprocessors
International Journal of Parallel Programming
Network Routing: Algorithms, Protocols, and Architectures
Network Routing: Algorithms, Protocols, and Architectures
Modeling Toroidal Networks with the Gaussian Integers
IEEE Transactions on Computers
On routing in circulant graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Twisted Torus Topologies for Enhanced Interconnection Networks
IEEE Transactions on Parallel and Distributed Systems
Handbook of Product Graphs, Second Edition
Handbook of Product Graphs, Second Edition
Generalized Recursive Circulant Graphs
IEEE Transactions on Parallel and Distributed Systems
Perfect Codes for Metrics Induced by Circulant Graphs
IEEE Transactions on Information Theory
Hamiltonian Decomposition of the Rectangular Twisted Torus
IEEE Transactions on Parallel and Distributed Systems
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Whereas the maximum number of vertices in a four-regular circulant of diameter a is 2a^2+2a+1, the bound turns out to be 2a^2 if the condition of bipartiteness is imposed. Tzvieli presented a family of @j(a) such dense bipartite circulants on 2a^2 vertices for each a=3, where @j(a) denotes the number of positive integers less than or equal to @?12(a-1)@? that are coprime with a. The present paper shows that each of those graphs is obtainable from the 2axa rectangular twisted torus by appropriately trading a maximum of 2a edges for as many new edges. The underlying structural similarity between the two graphs leads to a simple intuitive routing algorithm for the circulants. The result closely parallels the routing in dense nonbipartite circulants on 2a^2+2a+1 vertices. Additional results include a set of vertex-disjoint paths between every pair of distinct vertices in the circulants, and a proof that the 2axa rectangular twisted torus itself is probably not a circulant.