Abstract
A graph is weakly perfect if its clique number and chromatic number are equal. We show that the enhanced power graph of a finite group G is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of G. The proof requires a combinatorial lemma. We give some remarks about related graphs.
| Original language | English |
|---|---|
| Pages (from-to) | 100-105 |
| Number of pages | 6 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 85 |
| Issue number | 1 |
| Early online date | 29 Nov 2022 |
| Publication status | Published - 1 Feb 2023 |
Keywords
- Enhanced power graph
- Weakly perfect graph
- Finite group
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