Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
DOI: 10.82366/162
Author: Ait Elhadi, Djamila
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7075994164
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