The n-Total Graph of an Integral Domain
A Master of Science thesis in Mathematics by Myriam Abi Habib entitled, “The n-Total Graph of an Integral Domain”, submitted in May 2025. Thesis advisor is Dr. Ayman Badawi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form).
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | doctoralThesis |
| منشور في: |
2025
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/11073/26118 |
| الوسوم: |
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| _version_ | 1864513432460460032 |
|---|---|
| author | Abi Habib, Myriam |
| author_facet | Abi Habib, Myriam |
| author_role | author |
| dc.contributor.none.fl_str_mv | Badawi, Ayman |
| dc.creator.none.fl_str_mv | Abi Habib, Myriam |
| dc.date.none.fl_str_mv | 2025-06-12T14:07:10Z 2025-06-12T14:07:10Z 2025-05 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | 29.232-2025.05 https://hdl.handle.net/11073/26118 |
| dc.language.none.fl_str_mv | en_US |
| dc.subject.none.fl_str_mv | n-Total graph Integral domain Prime ideal |
| dc.title.none.fl_str_mv | The n-Total Graph of an Integral Domain |
| 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 Myriam Abi Habib entitled, “The n-Total Graph of an Integral Domain”, submitted in May 2025. Thesis advisor is Dr. Ayman Badawi. Soft copy is available (Thesis, Completion Certificate, Approval Signatures, and AUS Archives Consent Form). |
| format | doctoralThesis |
| id | aus_9a2af09909b7318d865da520b1a1cccd |
| identifier_str_mv | 29.232-2025.05 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/26118 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | The n-Total Graph of an Integral DomainAbi Habib, Myriamn-Total graphIntegral domainPrime idealA Master of Science thesis in Mathematics by Myriam Abi Habib entitled, “The n-Total Graph of an Integral Domain”, submitted in May 2025. 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 an integral domain, denoted by n-TG(R) where R is an integral domain i.e. the only zero divisor of the ring R is 0. The n-total graph is an undirected graph with vertex set R. Two vertices x and y are connected by an edge if xⁿ + yⁿ Є D where D is a prime ideal or the union of prime ideals. This study will explore both the graph-theoretical and ring-theoretical properties of the n-total graph of an integral domain or a product of integral domains, such as connectedness, completeness, diameter and girth.College of Arts and SciencesDepartment of Mathematics and StatisticsMaster of Science in Mathematics (MSMTH)Badawi, Ayman2025-06-12T14:07:10Z2025-06-12T14:07:10Z2025-05info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdf29.232-2025.05https://hdl.handle.net/11073/26118en_USoai:repository.aus.edu:11073/261182025-11-11T07:05:37Z |
| spellingShingle | The n-Total Graph of an Integral Domain Abi Habib, Myriam n-Total graph Integral domain Prime ideal |
| status_str | publishedVersion |
| title | The n-Total Graph of an Integral Domain |
| title_full | The n-Total Graph of an Integral Domain |
| title_fullStr | The n-Total Graph of an Integral Domain |
| title_full_unstemmed | The n-Total Graph of an Integral Domain |
| title_short | The n-Total Graph of an Integral Domain |
| title_sort | The n-Total Graph of an Integral Domain |
| topic | n-Total graph Integral domain Prime ideal |
| url | https://hdl.handle.net/11073/26118 |