New dense families of triple loop networks (Q1292809)

Multi-loop digraphs are widely studied because of their symmetric properties and their applications to loop networks. The problem is to find the maximum number of vertices for a fixed value of the diameter. For double-loop digraphs, all optimal families have been found by using a geometrical approach. For triple-loop digraphs, only some dense, but possibly not optimal, families are known. In the present paper, some new dense families are given for triple-loop digraphs using a geometrical approach. These families improve previous known results.