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The Optimization of Chordal Ring

This paper deals with the design of multi-(micro)computer interconnection networks modelled by graphs. In particular we concentrate upon the optimization of a new family of such networks that turn out to be a generalization of the well-known Arden and Lee's chordal ring networks. This optimization problem leads to the search for certain 3-regular graphs with minimum diameter for a given order and/or maximum order for a given diameter. The use of a geometrical approach based on plane tessellations facilitates the solution of the problem.