Automorphism group of the reduced power (di)graph of a finite group

TL;DR

This paper determines the automorphism groups of directed and undirected reduced power graphs of finite groups, providing explicit computations for various classes and exploring their relations to power graph automorphisms.

Contribution

It offers a complete description of automorphism groups of reduced power graphs for finite groups and relates them to power graph automorphisms, advancing understanding of graph symmetries in group theory.

Findings

Automorphism groups of reduced power graphs are explicitly characterized.

Computed automorphism groups for several classes of finite groups.

Established relations between reduced power graph automorphisms and power graph automorphisms.

Abstract

We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we establish some relation between the automorphism group of the undirected reduced power graph (resp. the directed reduced power graph) and the automorphism group of the undirected power graph (resp. the directed power graph) of a finite group.