A Note on Consistent Rotation Maps of Graph Cartesian Products

TL;DR

This paper presents a simple, rule-based method for constructing consistent rotation maps of the Cartesian product of two regular graphs, assuming the individual maps are already known.

Contribution

It introduces a constructive, rule-based approach for deriving consistent rotation maps of graph Cartesian products from existing maps.

Findings

Provides a set of addition and lookup rules for the construction

Enables systematic creation of rotation maps for product graphs

Assumes prior construction of component rotation maps

Abstract

Given two regular graphs with consistent rotation maps, we produce a constructive method for a consistent rotation map on their Cartesian product. This method will be given as a simple set of rules of addition and table look ups. We assume that the combinatorial construction of both consistent rotation maps has occurred before we construct the Cartesian product.