A new operation on digraphs : the Manhattan product

The Manhattan product of digraphs

We study the main properties of a new product of bipartite digraphs which we call Manhattan product. This product allows us to understand the subjacent product in the Manhattan street networks and can be used to built other networks with similar good properties. It is shown that if all the factors of such a product are (directed) cycles, then the digraph obtained is a Manhattan street network, ...

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).

More skew-equienergetic digraphs

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.

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