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arXiv · 2502.15967

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

Abbas Mohammadian·Ismail Guloglu·Ahmad Erfanian·Mark L. Lewis
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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.

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Abbas Mohammadian, Ismail Guloglu, Ahmad Erfanian, Mark L. Lewis. 2025-03-10. Generalizing the enhanced power graph of a group with respect to automorphisms. https://arxiv.org/abs/2502.15967

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