# Recognizing and testing isomorphism of Cayley graphs over an abelian group of order $4p$ in polynomial time

## TL;DR

This paper presents a polynomial-time algorithm for recognizing and testing isomorphism of Cayley graphs over an abelian group of order 4p, where p is prime, expanding efficient graph isomorphism solutions.

## Contribution

It introduces a polynomial-time algorithm for recognizing Cayley graphs over abelian groups of order 4p, extending previous results for circulant graphs.

## Key findings

- Recognition and isomorphism testing of Cayley graphs over abelian groups of order 4p is polynomial-time solvable.
- The algorithm applies to graphs with 4p vertices, where p is prime.
- This work generalizes known results for circulant graphs.

## Abstract

We construct a polynomial-time algorithm that given a graph $X$ with $4p$ vertices ($p$ is prime), finds (if any) a Cayley representation of $X$ over the group $C_2\times C_2\times C_p$. This result, together with the known similar result for circulant graphs, shows that recognising and testing isomorphism of Cayley graphs over an abelian group of order $4p$ can be done in polynomial time.