On Multiplicative Regular Graphs of Commutative Rings

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Haval Amin Mohammed
Adil Kadir Jabbar

Abstract

Background:


The zero-divisor graph is central in algebraic graph theory. Let be a commutative ring with identity. In this work we define the multiplicative regular graph as a generalization that captures the behavior of regular elements, those satisfying or.


Materials and Methods:


The graph  is defined using ring-theoretic conditions and graph-theoretic representations, Two distinct none-zero elements  and  are adjacent if and only if . A Python-based algorithm is used to construct and visualize  for finite commutative rings.


Results:


We prove that  if and only if , and  when  is a regular ring. The study includes analysis of key graph invariants such as connectivity, diameter, girth, and regularity.


Conclusion:


The graph offers a generalization of existing graphs of commutative rings. By emphasizing regular elements, this model uncovers new structural relationships within the ring and explores ring-theoretic properties through graph-theoretic methods.

Article Details

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Articles

How to Cite

[1]
“On Multiplicative Regular Graphs of Commutative Rings”, JUBPAS, vol. 33, no. 2, pp. 211–226, Jun. 2025, doi: 10.29196/jubpas.v33i2.5794.

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