# Directed Graphs of Cayley Functions

## TL;DR

This paper establishes a condition under which functions commuting with an idempotent on an infinite set are characterized as Cayley functions via their functional digraphs, advancing understanding of their algebraic structure.

## Contribution

It introduces a specific condition linking commuting functions and Cayley functions through their functional digraphs, providing new insights into their structure.

## Key findings

- Identifies a condition for functions to be Cayley functions
- Uses functional digraphs to characterize Cayley functions
- Advances theoretical understanding of function commutation on infinite sets

## Abstract

In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.