The (\Delta,D) and (\Delta,N) problems for New Amsterdam and Manhattan   digraphs
  We give a quasi-complete solution of the (\Delta,N) problem for two well-known families of digraphs used as good models for large interconnection networks. In our study we also relate both families, the New Amsterdam and Manhattan digraphs, with the double-step graphs (or circulant graphs with degree two). 
C. Dalf\'o, M.A. Fiol
math.CO cs.DM