Tripotent Divisor Graph of a Commutative Ring
In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/1954058 |
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| author | Luma A. Khaleel Husam Q. Mohammad Nazar H. Shuker |
| author_facet | Luma A. Khaleel Husam Q. Mohammad Nazar H. Shuker |
| author_sort | Luma A. Khaleel |
| collection | DOAJ |
| description | In this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR. We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph-theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields. |
| format | Article |
| id | doaj-art-911504960de440eea5fb56e1748fcbb9 |
| institution | OA Journals |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-911504960de440eea5fb56e1748fcbb92025-08-20T02:09:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/1954058Tripotent Divisor Graph of a Commutative RingLuma A. Khaleel0Husam Q. Mohammad1Nazar H. Shuker2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this work, we introduce a new concept called the tripotent divisor graph of a commutative ring. It is defined with vertices set in a ring R, where distinct vertices r1 and r2 are connected by an edge if their product belongs to the set of all nonunite tripotent in R. We denote this graph as 3I ΓR. We utilize this graph to examine the role of tripotent elements in the structure of rings. Additionally, we provide various findings regarding graph-theoretic characteristics of this graph, including its diameter, vertex degrees, and girth. Furthermore, we investigate the size, central vertices, and distances between vertices for the tripotent divisor graph formed by the direct product of two fields.http://dx.doi.org/10.1155/2024/1954058 |
| spellingShingle | Luma A. Khaleel Husam Q. Mohammad Nazar H. Shuker Tripotent Divisor Graph of a Commutative Ring International Journal of Mathematics and Mathematical Sciences |
| title | Tripotent Divisor Graph of a Commutative Ring |
| title_full | Tripotent Divisor Graph of a Commutative Ring |
| title_fullStr | Tripotent Divisor Graph of a Commutative Ring |
| title_full_unstemmed | Tripotent Divisor Graph of a Commutative Ring |
| title_short | Tripotent Divisor Graph of a Commutative Ring |
| title_sort | tripotent divisor graph of a commutative ring |
| url | http://dx.doi.org/10.1155/2024/1954058 |
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