On Multiplicative Regular Graphs of Commutative Rings

Haval Amin Mohammed; Adil Kadir Jabbar

doi:10.29196/jubpas.v33i2.5794

Article Details

On Multiplicative Regular Graphs of Commutative Rings

Authors:

Haval Amin Mohammed | Adil Kadir Jabbar

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.33 Issue 2, pp.211-226

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001383319

pISSN:

2312-8135

DOI:

10.29196/jubpas.v33i2.5794

Keywords:

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

On Multiplicative Regular Graphs of Commutative Rings

Authors:

Haval Amin Mohammed | Adil Kadir Jabbar

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.33 Issue 2, pp.211-226

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001383319

pISSN:

2312-8135

DOI:

10.29196/jubpas.v33i2.5794

Multiplicative regular graph

connectivity of a graph

regularity of a graph

diameter of a graph

girth of a graph

Issues

Article Details

On Multiplicative Regular Graphs of Commutative Rings

Authors: Haval Amin Mohammed | Adil Kadir Jabbar

Publisher: University of Babylon

Journal: JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.33 Issue 2, pp.211-226

Document Type: Article

Publication Date: 6/2025

Document Language: English

Document ID (Org No.): 2001383319

pISSN: 2312-8135

DOI: 10.29196/jubpas.v33i2.5794

Multiplicative regular graph

connectivity of a graph

regularity of a graph

diameter of a graph

girth of a graph

Issues

Authors:

Haval Amin Mohammed | Adil Kadir Jabbar

Publisher:

University of Babylon

Journal:

JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences Vol.33 Issue 2, pp.211-226

Document Type:

Article

Publication Date:

6/2025

Document Language:

English

Document ID (Org No.):

2001383319

pISSN:

2312-8135

DOI:

10.29196/jubpas.v33i2.5794