Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 1, No 1 (2013): Electronic Journal of Graph Theory and Applications

The Manhattan product of digraphs

Francesc Comellas (Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Barcelona, Catalonia)
Cristina Dalfo (Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Barcelona, Catalonia)
Miquel Àngel Fiol (Departament de Matematica Aplicada IV, Universitat Politecnica de Catalunya, Barcelona, Catalonia)



Article Info

Publish Date
30 Apr 2013

Abstract

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, a widely studied topology for modeling some interconnection networks. To this respect, it is proved that many properties of these networks, such as high symmetries, reduced diameter and the presence of Hamiltonian cycles, are shared by the Manhattan product of some digraphs. Moreover, we show that the Manhattan product of two Manhattan streets networks is also a Manhattan street network. Finally, some sufficient conditions for the Manhattan product of two Cayley digraphs to be also a Cayley digraph are given. Throughout our study we use some interesting recent concepts, such as the unilateral distance and related graph invariants.

Copyrights © 2013






Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...