New results for the degree/diameter problem

The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs'' is in the design of efficient communication network topologies.Comment: 15 page

Connections between two cycles — a new design of dense processor interconnection networks

AbstractIn this paper we attempt to maximize the order of graphs of given degree Δ and diameter D. These graphs, which are known as (Δ, 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 our method. Again, the improvement of the lower bounds is significant