Generalizing the enhanced power graph of a group with respect to automorphisms

We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the enhanced power graph. We consider the universal vertices of this graph and when this graph is a complete graph. Finally, we classify when this graph is the empty graph.

Publication Details

Journal
ArXiv.org
Published
2025-02-21
Primary Topic
Finite Group Theory Research
Type
article
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article

Generalizing the enhanced power graph of a group with respect to automorphisms

ArXiv.org
Finite Group Theory Research
article

Generalizing the enhanced power graph of a group with respect to automorphisms

article en

Abstract

We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the enhanced power graph. We consider the universal vertices of this graph and when this graph is a complete graph. Finally, we classify when this graph is the empty graph.

ArXiv.org
Openalex Percentile: Top 42%
Finite Group Theory Research
Open Access PDFOpenAlex
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Generalizing the enhanced power graph of a group with respect to automorphisms · ArXiv.org (2025) | TGRS Research Map | TGRS