Quasi-Regular Graphs Associated with Commutative Rings
One of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented. In this paper, we define an innovative graph on rings, explore its characteristics, and examine...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6209466 |
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| _version_ | 1832554750481006592 |
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| author | Nasr Zeyada Najat Muthana Sultanah Al-Rashidi |
| author_facet | Nasr Zeyada Najat Muthana Sultanah Al-Rashidi |
| author_sort | Nasr Zeyada |
| collection | DOAJ |
| description | One of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented. In this paper, we define an innovative graph on rings, explore its characteristics, and examine how it relates to other notions in the field. Let S be a ring; the quasi-regular graph of S is a graph with a vertex set of S−0 and any two different vertices w and z are adjacent if 1−wz is a unit in S. We study this graph by providing different examples and proving some crucial characteristics. This study provides important results and paves the way for a lot of different inquiries and studies utilizing this novel approach. |
| format | Article |
| id | doaj-art-291bb626d2de44e1b6f600549805c605 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-291bb626d2de44e1b6f600549805c6052025-02-03T05:50:38ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6209466Quasi-Regular Graphs Associated with Commutative RingsNasr Zeyada0Najat Muthana1Sultanah Al-Rashidi2Department of MathematicsDepartment of MathematicsDepartment of MathematicsOne of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented. In this paper, we define an innovative graph on rings, explore its characteristics, and examine how it relates to other notions in the field. Let S be a ring; the quasi-regular graph of S is a graph with a vertex set of S−0 and any two different vertices w and z are adjacent if 1−wz is a unit in S. We study this graph by providing different examples and proving some crucial characteristics. This study provides important results and paves the way for a lot of different inquiries and studies utilizing this novel approach.http://dx.doi.org/10.1155/2022/6209466 |
| spellingShingle | Nasr Zeyada Najat Muthana Sultanah Al-Rashidi Quasi-Regular Graphs Associated with Commutative Rings Journal of Mathematics |
| title | Quasi-Regular Graphs Associated with Commutative Rings |
| title_full | Quasi-Regular Graphs Associated with Commutative Rings |
| title_fullStr | Quasi-Regular Graphs Associated with Commutative Rings |
| title_full_unstemmed | Quasi-Regular Graphs Associated with Commutative Rings |
| title_short | Quasi-Regular Graphs Associated with Commutative Rings |
| title_sort | quasi regular graphs associated with commutative rings |
| url | http://dx.doi.org/10.1155/2022/6209466 |
| work_keys_str_mv | AT nasrzeyada quasiregulargraphsassociatedwithcommutativerings AT najatmuthana quasiregulargraphsassociatedwithcommutativerings AT sultanahalrashidi quasiregulargraphsassociatedwithcommutativerings |