Bandwidth and pathwidth of three-dimensional grids

TL;DR

This paper determines the bandwidth and pathwidth of three-dimensional and multi-dimensional grids, extending known results from cubic cases and linking these parameters to the vertex boundary width.

Contribution

It introduces a method to compute bandwidth and pathwidth for multi-dimensional grids using vertex boundary width, including cases with large maximum factors.

Findings

Bandwidth and pathwidth of 3D grids are explicitly determined.

Bandwidth equals pathwidth for these grid graphs.

Results extend to multi-dimensional grids with large maximum factors.

Abstract

We study the bandwidth and the pathwidth of multi-dimensional grids. It can be shown for grids, that these two parameters are equal to a more basic graph parameter, the vertex boundary width. Using this fact, we determine the bandwidth and the pathwidth of three-dimensional grids, which were known only for the cubic case. As a by-product, we also determine the two parameters of multi-dimensional grids with relatively large maximum factors.