Forbidden subgraphs in enhanced power graphs of finite groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911836568289280 |
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| author | Ma, Xuanlong Zahirović, Samir Lv, Yubo She, Yanhong |
| author_facet | Ma, Xuanlong Zahirović, Samir Lv, Yubo She, Yanhong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_04754 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Forbidden subgraphs in enhanced power graphs of finite groups Ma, Xuanlong Zahirović, Samir Lv, Yubo She, Yanhong Combinatorics 05C25, 05C38 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. |
| title | Forbidden subgraphs in enhanced power graphs of finite groups |
| topic | Combinatorics 05C25, 05C38 |
| url | https://arxiv.org/abs/2104.04754 |