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As a result of recent technological developments there is an increasing interest in the interconnection of microcomputers through networks. For general computation the interconnection graphs should have short internode communication paths and should be of low degree, systematically structured, and incrementally extensible. A family of graphs, called multitree structured (MTS) having these properties is presented. The MTS graphs of degree three have the maximum number of nodes, known to date, for given diameters.