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Quasi-Regular Graphs Associated with Commutative Rings

Author

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  • Nasr Zeyada
  • Najat Muthana
  • Sultanah Al-Rashidi
  • Francesca Tartarone

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.

Suggested Citation

  • Nasr Zeyada & Najat Muthana & Sultanah Al-Rashidi & Francesca Tartarone, 2022. "Quasi-Regular Graphs Associated with Commutative Rings," Journal of Mathematics, Hindawi, vol. 2022, pages 1-5, August.
    • Handle: RePEc:hin:jjmath:6209466
    DOI: 10.1155/2022/6209466
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