The Manhattan product of digraphs

A new operation on digraphs : the Manhattan product

We give a formal definition of a new product of bipartite digraphs, the Manhattan product, and we study some of its main properties. It is shown that if all the factors of the above product are (directed) cycles, then the digraph obtained is a Manhattan street network. To this respect, it is proved that many properties of these networks, such as high symmetries and the presence of Hamiltonian c...

Manhattan Product of Digraphs

We review the Manhattan product of digraphs from the viewpoint of spectral analysis and obtain some preliminary formulae. As an example, the spectrum of the Manhattan product of the directed path Pn and the directed cycle C2 is obtained as well as its asymptotic spectral distribution.

The (\Delta,D) and (\Delta,N) problems for New Amsterdam and Manhattan digraphs

We give a quasi-complete solution of the (∆, 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).

The Spectra of Manhattan Street Networks

The multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dime...

The (Δ,D) and (Δ,N) problems for New Amsterdam and Manhattan digraphs