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The n-Total Graph of an Integral Domain
Abi Habib, Myriam
Abi Habib, Myriam
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).
Abstract
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.