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: Ali Al Khabyah, Kholood Alnefaie, Shabir Ahmad Mir, Nadeem ur Rehman, Junaid Nisar
Format: Article
Language:English
Published: Taylor & Francis Group 2025-08-01
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.
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issn 0972-8600
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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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AT kholoodalnefaie linegraphembeddingofcointersectiongraphofidealsofcommutativerings
AT shabirahmadmir linegraphembeddingofcointersectiongraphofidealsofcommutativerings
AT nadeemurrehman linegraphembeddingofcointersectiongraphofidealsofcommutativerings
AT junaidnisar linegraphembeddingofcointersectiongraphofidealsofcommutativerings