# On Cayley graphs of algebraic structures

## TL;DR

This paper provides simple graph-theoretic characterizations of Cayley graphs for various algebraic structures, including monoids, groups, and quasigroups, and demonstrates their effectiveness for finite degree end-regular graphs.

## Contribution

It introduces new characterizations of Cayley graphs for multiple algebraic structures and applies them to finite degree end-regular graphs.

## Key findings

- Characterizations are effective for finite degree end-regular graphs.
- Unified approach for various algebraic structures.
- Simplifies understanding of Cayley graph structures.

## Abstract

We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.