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

TL;DR

This paper provides a near-complete solution to the (,N) problem for New Amsterdam and Manhattan digraphs, linking them to double-step and circulant graphs, advancing understanding of their interconnection network properties.

Contribution

It offers a quasi-complete solution to the (,N) problem for these digraphs and relates them to well-studied circulant graphs, enriching graph theory and network design.

Findings

Solved the (,N) problem for New Amsterdam and Manhattan digraphs

Established connections between these digraphs and circulant graphs

Enhanced understanding of their structural properties

Abstract

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).