Finite groups whose coprime graph is split, threshold, chordal, or a cograph
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 group...
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Estonian Academy Publishers
2024-10-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
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| author | Jin Chen Shixun Lin Xuanlong Ma |
| author_facet | Jin Chen Shixun Lin Xuanlong Ma |
| author_sort | Jin Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3fced52ea93b48f3ad61f26bbb4fd1ce |
| institution | Kabale University |
| issn | 1736-6046 1736-7530 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Estonian Academy Publishers |
| record_format | Article |
| series | Proceedings of the Estonian Academy of Sciences |
| spelling | doaj-art-3fced52ea93b48f3ad61f26bbb4fd1ce2024-11-22T14:17:30ZengEstonian Academy PublishersProceedings of the Estonian Academy of Sciences1736-60461736-75302024-10-01734323331https://doi.org/10.3176/proc.2024.4.01https://doi.org/10.3176/proc.2024.4.01Finite groups whose coprime graph is split, threshold, chordal, or a cographJin Chen0Shixun Lin1Xuanlong Ma2School of Mathematics and Statistics, Zhaotong University, Zhaotong 657000, ChinaSchool of Mathematics and Statistics, Zhaotong University, Zhaotong 657000, P. R. China; School of Science, China University of Geosciences (Beijing), Beijing 100083, P. R. ChinaSchool of Science, Xi’an Shiyou University, Xi’an 710065, ChinaGiven 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.https://kirj.ee/wp-content/plugins/kirj/pub/proc-4-2024-323-331_20241003103848.pdfcoprime graphssplit graphscographsthreshold graphschordal graphsfinite group |
| spellingShingle | Jin Chen Shixun Lin Xuanlong Ma Finite groups whose coprime graph is split, threshold, chordal, or a cograph Proceedings of the Estonian Academy of Sciences coprime graphs split graphs cographs threshold graphs chordal graphs finite group |
| title | Finite groups whose coprime graph is split, threshold, chordal, or a cograph |
| title_full | Finite groups whose coprime graph is split, threshold, chordal, or a cograph |
| title_fullStr | Finite groups whose coprime graph is split, threshold, chordal, or a cograph |
| title_full_unstemmed | Finite groups whose coprime graph is split, threshold, chordal, or a cograph |
| title_short | Finite groups whose coprime graph is split, threshold, chordal, or a cograph |
| title_sort | finite groups whose coprime graph is split threshold chordal or a cograph |
| topic | coprime graphs split graphs cographs threshold graphs chordal graphs finite group |
| url | https://kirj.ee/wp-content/plugins/kirj/pub/proc-4-2024-323-331_20241003103848.pdf |
| work_keys_str_mv | AT jinchen finitegroupswhosecoprimegraphissplitthresholdchordaloracograph AT shixunlin finitegroupswhosecoprimegraphissplitthresholdchordaloracograph AT xuanlongma finitegroupswhosecoprimegraphissplitthresholdchordaloracograph |