Boxicity of power graphs of arbitrary groups

Determine the boxicity of the power graph Pow(G) for arbitrary finite groups G, beyond the cyclic groups analyzed through their reduced power graphs and corresponding divisor graphs.

Background

A power graph Pow(G) has the elements of a finite group G as vertices, with two vertices adjacent when one is a positive-integer power of the other. The paper establishes a relationship between the power graph of a finite cyclic group and the divisor graph D(n), showing that their boxicities coincide via the reduced power graph.

The analysis in the paper is restricted to cyclic groups. Extending the determination of boxicity to power graphs of arbitrary finite groups is explicitly left unresolved.