Line graph embedding of co-intersection graph of ideals of commutative rings
This research paper focuses on the co-intersection graph of a commutative ring [Formula: see text]. The co-intersection graph of [Formula: see text] denoted by [Formula: see text] is a simple graph with vertices that are non-trivial ideals of [Formula: see text], and two distinct vertices I and J ar...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-08-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2025.2534342 |
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| author | Ali Al Khabyah Kholood Alnefaie Shabir Ahmad Mir Nadeem ur Rehman Junaid Nisar |
| author_facet | Ali Al Khabyah Kholood Alnefaie Shabir Ahmad Mir Nadeem ur Rehman Junaid Nisar |
| author_sort | Ali Al Khabyah |
| collection | DOAJ |
| description | This research paper focuses on the co-intersection graph of a commutative ring [Formula: see text]. The co-intersection graph of [Formula: see text] denoted by [Formula: see text] is a simple graph with vertices that are non-trivial ideals of [Formula: see text], and two distinct vertices I and J are adjacent if and only if [Formula: see text]. The primary goal of this study is to characterize Artinian commutative rings [Formula: see text], and determining whether their associated co-intersection graph [Formula: see text] forms a line graph and identifying instances where it becomes the complement of a line graph. Additionally, the article investigates the planarity and outerplanarity of the line graph of the co-intersection graph [Formula: see text]. Finally, the research identifies the genus one of this line graph of co-intersection graph of ideals of a commutative ring. |
| format | Article |
| id | doaj-art-d343cdd39b78478990742e5ce3570bc1 |
| institution | DOAJ |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-d343cdd39b78478990742e5ce3570bc12025-08-20T03:03:51ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-08-011910.1080/09728600.2025.2534342Line graph embedding of co-intersection graph of ideals of commutative ringsAli Al Khabyah0Kholood Alnefaie1Shabir Ahmad Mir2Nadeem ur Rehman3Junaid Nisar4Department of Mathematics, College of Science, King Khalid University, Abha, Saudi ArabiaDepartment of Mathematics, College of Science, Taibah University, Madinah, Saudi ArabiaSchool of Basic and Applied Sciences, Faculty of Science and Technology, JSPM University, Pune, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh, IndiaDepartment of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune, IndiaThis research paper focuses on the co-intersection graph of a commutative ring [Formula: see text]. The co-intersection graph of [Formula: see text] denoted by [Formula: see text] is a simple graph with vertices that are non-trivial ideals of [Formula: see text], and two distinct vertices I and J are adjacent if and only if [Formula: see text]. The primary goal of this study is to characterize Artinian commutative rings [Formula: see text], and determining whether their associated co-intersection graph [Formula: see text] forms a line graph and identifying instances where it becomes the complement of a line graph. Additionally, the article investigates the planarity and outerplanarity of the line graph of the co-intersection graph [Formula: see text]. Finally, the research identifies the genus one of this line graph of co-intersection graph of ideals of a commutative ring.https://www.tandfonline.com/doi/10.1080/09728600.2025.2534342Co-intersection graphline graphcomplement of a line graphplanaritygenusArtinian local rings |
| spellingShingle | Ali Al Khabyah Kholood Alnefaie Shabir Ahmad Mir Nadeem ur Rehman Junaid Nisar Line graph embedding of co-intersection graph of ideals of commutative rings AKCE International Journal of Graphs and Combinatorics Co-intersection graph line graph complement of a line graph planarity genus Artinian local rings |
| title | Line graph embedding of co-intersection graph of ideals of commutative rings |
| title_full | Line graph embedding of co-intersection graph of ideals of commutative rings |
| title_fullStr | Line graph embedding of co-intersection graph of ideals of commutative rings |
| title_full_unstemmed | Line graph embedding of co-intersection graph of ideals of commutative rings |
| title_short | Line graph embedding of co-intersection graph of ideals of commutative rings |
| title_sort | line graph embedding of co intersection graph of ideals of commutative rings |
| topic | Co-intersection graph line graph complement of a line graph planarity genus Artinian local rings |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2025.2534342 |
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