An elementary proof of a conjecture on graph-automorphism

TL;DR

This paper provides an elementary combinatorial proof for a conjecture regarding the automorphism group of the power graph of finite cyclic groups, addressing a problem proposed in 2013.

Contribution

It offers a new, simplified proof of a conjecture about automorphism groups in graph theory, specifically for power graphs of cyclic groups.

Findings

Confirmed the conjecture for finite cyclic groups

Provided an elementary combinatorial proof

Enhanced understanding of automorphism groups in graph theory

Abstract

In this article, we give an elementary combinatorial proof of a conjecture about the determination of automorphism group of the power graph of finite cyclic groups, proposed by Doostabadi, Erfanian and Jafarzadeh in 2013.