Connections between two cycles-A new design of dense processor interconnection networks

In this paper the authors attempt to maximize the order of graphs of given degree ℝ and diameter D. These graphs, which are known as (ℝ,D) graphs, are used as dense interconnection networks, i.e., processors with relatively few links are connected with relatively short paths. The method described in this paper uses periodic connections between two cycles of the same length. The results obtained give a significant improvement of the known lower bounds in many cases. Large bipartite graphs with a given degree and diameter were also obtained by the presents method. Again, the improvement of the lower bounds is significant.