On connected components and perfect codes of proper order graphs of finite groups
| Autor: | Huani Li, Shixun Lin, Xuanlong Ma |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Proceedings of the Estonian Academy of Sciences, Vol 73, Iss 1, Pp 68-76 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1736-6046 1736-7530 |
| DOI: | 10.3176/proc.2024.1.08 |
| Popis: | Let G be a finite group with the identity element e. The proper order graph of G, denoted by â* (G), is an undirected graph with a vertex set G \ {e}, where two distinct vertices x and y are adjacent whenever o(x) | o(y) or o(y) | o(x), where o(x) and o(y) are the orders of x and y, respectively. This paper studies the perfect codes of â*(G). We characterize all connected components of a proper order graph and give a necessary and sufficient condition for a connected proper order graph. We also determine the perfect codes of the proper order graphs of a few classes of finite groups, including nilpotent groups, CP-groups, dihedral groups and generalized quaternion groups. |
| Databáze: | Directory of Open Access Journals |
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