Power Graph Classes and Overfullness
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913972360314880 |
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| author | Feinsilber, Elie |
| author_facet | Feinsilber, Elie |
| contents | In this paper, we investigate the edge-coloring number of the power graph of a finite group. We characterize which finite groups have overfull power graphs, showing that this occurs if and only if the group is cyclic of odd prime power order. We then show that this classsifies the class of power graphs: The power graph of a finite group is Class 2 if and only if the group is cyclic of odd prime power order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power Graph Classes and Overfullness Feinsilber, Elie Group Theory Combinatorics 05C25 (Primary), 05C15 (Secondary) In this paper, we investigate the edge-coloring number of the power graph of a finite group. We characterize which finite groups have overfull power graphs, showing that this occurs if and only if the group is cyclic of odd prime power order. We then show that this classsifies the class of power graphs: The power graph of a finite group is Class 2 if and only if the group is cyclic of odd prime power order. |
| title | Power Graph Classes and Overfullness |
| topic | Group Theory Combinatorics 05C25 (Primary), 05C15 (Secondary) |
| url | https://arxiv.org/abs/2508.01417 |