The n-Total Graph of a Commutative Ring
A Master of Science thesis in Mathematics by Djamila Ait Elhadi entitled, “The n-Total Graph of a Commutative Ring”, submitted in November 2024. Thesis advisor is Dr. Ayman Badawi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
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| Format: | doctoralThesis |
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2024
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| Online Access: | https://hdl.handle.net/11073/25859 |
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| _version_ | 1864513439222726656 |
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| author | Ait Elhadi, Djamila |
| author_facet | Ait Elhadi, Djamila |
| author_role | author |
| dc.contributor.none.fl_str_mv | Badawi, Ayman |
| dc.creator.none.fl_str_mv | Ait Elhadi, Djamila |
| dc.date.none.fl_str_mv | 2024-11 2025-02-12T07:04:40Z 2025-02-12T07:04:40Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2024.09 https://hdl.handle.net/11073/25859 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | Commutative rings Total graph Regular elements Zero-divisors |
| dc.title.none.fl_str_mv | The n-Total Graph of a Commutative Ring |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/doctoralThesis |
| description | A Master of Science thesis in Mathematics by Djamila Ait Elhadi entitled, “The n-Total Graph of a Commutative Ring”, submitted in November 2024. Thesis advisor is Dr. Ayman Badawi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form). |
| format | doctoralThesis |
| id | aus_87f733dfec564756bcd8d92e7668dd9a |
| identifier_str_mv | 29.232-2024.09 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/25859 |
| publishDate | 2024 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | The n-Total Graph of a Commutative RingAit Elhadi, DjamilaCommutative ringsTotal graphRegular elementsZero-divisorsA Master of Science thesis in Mathematics by Djamila Ait Elhadi entitled, “The n-Total Graph of a Commutative Ring”, submitted in November 2024. Thesis advisor is Dr. Ayman Badawi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).Let n ≥ 1. This thesis introduces the n-total graph of a commutative ring R. The n-total graph of a commutative ring R, denoted by n ─ T(R), is an undirected simple graph with vertex set R, such that two vertices x; y in R are connected by an edge if xⁿ + yⁿ in Z(R). Note that if n = 1, then the 1-total graph of R is the total graph of R as in [7]. In this thesis, we study some graph properties, for example, connectedness, diameter, and girth, for the graph that we defined.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Badawi, Ayman2025-02-12T07:04:40Z2025-02-12T07:04:40Z2024-11info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2024.09https://hdl.handle.net/11073/25859en_USoai:repository.aus.edu:11073/258592025-11-11T07:05:36Z |
| spellingShingle | The n-Total Graph of a Commutative Ring Ait Elhadi, Djamila Commutative rings Total graph Regular elements Zero-divisors |
| status_str | publishedVersion |
| title | The n-Total Graph of a Commutative Ring |
| title_full | The n-Total Graph of a Commutative Ring |
| title_fullStr | The n-Total Graph of a Commutative Ring |
| title_full_unstemmed | The n-Total Graph of a Commutative Ring |
| title_short | The n-Total Graph of a Commutative Ring |
| title_sort | The n-Total Graph of a Commutative Ring |
| topic | Commutative rings Total graph Regular elements Zero-divisors |
| url | https://hdl.handle.net/11073/25859 |