English

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

Group Theory 2025-03-11 v2

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.

Keywords

Cite

@article{arxiv.2502.15967,
  title  = {Generalizing the enhanced power graph of a group with respect to automorphisms},
  author = {Abbas Mohammadian and Ismail Guloglu and Ahmad Erfanian and Mark L. Lewis},
  journal= {arXiv preprint arXiv:2502.15967},
  year   = {2025}
}

Comments

The introduction has been revised