On constructing infinite families of optimal double loop networks

Double-loop networks (DLN) have been widely studied as architecture for local area networks. A double-loop digraph G(N; 1, s) has the set of vertices V={0, 1,..., N-1} and the adjacencies are defined by v→v + 1(mod N) and v→v +s(mod N) for any v ∈ V. With the approach proposed by Li and Xu et al., we give some methods to find infinite families of optimal DLN from k-tight(k≥0) optimal DLN and prove that it is possible to find infinite families of optimal DLN from any optimal DLN for 4≤N<;2176. Also we give some optimal DLN, from which we can not construct any infinite family of optimal DLN yet. With these results, some errata in the bibliography are corrected.