# A description of automorphism group of power graphs of finite groups

## TL;DR

This paper characterizes the automorphism groups of power graphs for various classes of finite groups, providing a comprehensive understanding of their symmetries.

## Contribution

It introduces methods to determine automorphism groups of power graphs and applies them to all finite groups, including abelian, homocyclic, and nilpotent groups.

## Key findings

- Full automorphism group of power graphs for all finite groups described.
- Automorphism groups for abelian, homocyclic, and nilpotent groups explicitly determined.
- New techniques for analyzing graph automorphisms introduced.

## Abstract

The power graph of a group is the graph whose vertex set is the set of nontrivial elements of group, two elements being adjacent if one is a power of the other. We introduce some way for find the automorphism groups of some graphs. As an application We describe the full automorphism group of the power graph of all finite groups. Also we obtain the full automorphism group of power graph of abelian, homocyclic and nilpotent groups