Planarity of Cayley graphs of graph products of groups

TL;DR

This paper classifies when Cayley graphs of graph products of finite abelian groups are planar, providing a complete characterization based on the group's structure.

Contribution

It offers a complete classification of the planarity of Cayley graphs for graph products of finite abelian groups.

Findings

Identifies all finite abelian group graph products with planar Cayley graphs.

Provides criteria for planarity based on group structure.

Completes the classification problem for this class of groups.

Abstract

We obtain a complete classification of graph products of finite abelian groups whose Cayley graphs with respect to the standard presentations are planar.