Quasi-Regular Graphs Associated with Commutative Rings

Nasr Zeyada, Najat Muthana, Sultanah Al-Rashidi and Francesca Tartarone

Journal of Mathematics, 2022, vol. 2022, 1-5

Abstract: One of the most important branches of mathematics is algebraic graph theory, which solves graph problems with algebraic methods. In graph theory, several algebraic properties of a ring can be represented. In this paper, we define an innovative graph on rings, explore its characteristics, and examine how it relates to other notions in the field. Let S be a ring; the quasi-regular graph of S is a graph with a vertex set of S−0 and any two different vertices w and z are adjacent if 1−wz is a unit in S. We study this graph by providing different examples and proving some crucial characteristics. This study provides important results and paves the way for a lot of different inquiries and studies utilizing this novel approach.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6209466

DOI: 10.1155/2022/6209466

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