Enumerating typical abelian coverings of Cayley graphs

TL;DR

This paper completes the enumeration of typical abelian coverings of Cayley graphs by reducing the problem to counting specific subgroups within finite abelian groups.

Contribution

It introduces a reduction method that simplifies the enumeration of abelian coverings of Cayley graphs to subgroup enumeration in finite abelian groups.

Findings

Complete enumeration of typical abelian coverings achieved.

Reduction of the problem to subgroup enumeration in finite abelian groups.

Provides a framework for further enumeration and classification.

Abstract

In this article we complete the work of enumerating typical abelian coverings of Cayley graphs, by reducing the problem to enumerating certain subgroups of finite abelian groups.