Forbidden subgraphs in enhanced power graphs of finite groups
Abstract
The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal graphs and cographs. These results partly answer a question posed by Peter J. Cameron.
Cite
@article{arxiv.2104.04754,
title = {Forbidden subgraphs in enhanced power graphs of finite groups},
author = {Xuanlong Ma and Samir Zahirović and Yubo Lv and Yanhong She},
journal= {arXiv preprint arXiv:2104.04754},
year = {2024}
}
Comments
This paper has been accepted for publication in Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas. Note that this is not a finally version. Its finally version will soon appear in the journal's homepage