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:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Abi Habib, Myriam (author)
التنسيق: doctoralThesis
منشور في: 2025
الموضوعات:
الوصول للمادة أونلاين:https://hdl.handle.net/11073/26118
الوسوم: إضافة وسم
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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).
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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