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A family of regular graphs of degree 3, called Chordal Rings, is presented as a possible candidate for the implementation of a local network of message-connected (micro) computers. For a properly constructed graph in this family having n nodes the diameter, or maximum length message path, is shown to be of 0(n 1/2). The symmetry of the graphs makes it possible to determine message routing by using a simple distributed algorithm. The given algorithm is also potentially useful for the determination of alternate paths in the event of node or link failure.