Finite groups whose coprime graph is split, threshold, chordal, or a cograph
| Autor: | Jin Chen, 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 4, Pp 323-331 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1736-6046 1736-7530 |
| DOI: | 10.3176/proc.2024.4.01 |
| Popis: | Given a finite group G, the coprime graph of G, denoted by Î(G), is defined as an undirected graph with the vertex set G, and for distinct x, y â G, x is adjacent to y if and only if (o(x), o(y)) = 1, where o(x) and o(y) are the orders of x and y, respectively. This paper classifies the finite groups with split, threshold and chordal coprime graphs, as well as gives a characterization of the finite groups whose coprime graph is a cograph. As some applications, the paper classifies the finite groups G such that Î(G) is a cograph if G is a nilpotent group, a dihedral group, a generalized quaternion group, a symmetric group, an alternating group, or a sporadic simple group. |
| Databáze: | Directory of Open Access Journals |
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