Connected components in the invariably generating graph of a finite group

TL;DR

This paper demonstrates that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices, revealing complex connectivity properties.

Contribution

It establishes that the invariably generating graph can have unbounded connected components, a novel insight into the structure of finite groups.

Findings

The invariably generating graph can have arbitrarily many connected components.

Connected components can have at least two vertices.

The result applies to all finite groups.

Abstract

We prove that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices.