D-trees: A class of dense regular interconnection topologies

The authors propose a class of dense regular hierarchical interconnection topologies called D-trees. These topologies are denser than interconnection networks such as the ring and the n-dimensional Boolean hypercube and compare favorably with other proposed interconnection schemes, such as the star graph and the pancake graph. In addition, the class of topologies proposed is more flexible in that both the degree and the diameter can be varied in the construction of the required topology. These topologies are also incrementally scalable in the number of nodes that can be connected. Expressions are derived for the number of nodes that can be connected in this manner and the corresponding diameters of such topologies. They are also compared with the Boolean hypercube and the star graph.