On Beck’s zero-divisor graph

Deepa Sinha and Bableen Kaur
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 4, Pages 150—157
DOI: 10.7546/nntdm.2019.25.4.150-157
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Authors and affiliations

Deepa Sinha
Department of Mathematics, South Asian University
Akbar Bhawan, Chanakyapuri, New Delhi 110021, India

Bableen Kaur
Department of Mathematics, South Asian University
Akbar Bhawan, Chanakyapuri, New Delhi 110021, India

Abstract

For a commutative ring R with unity (1 ≠ 0), the zero-divisor graph of R, denoted by Γ(R), is a simple graph with vertices as elements of R and two distinct vertices are adjacent whenever the product of the vertices is zero. This article aims at gaining a deeper insight into the basic structural properties of zero-divisor graphs given by Beck.

Keywords

  • Commutative ring
  • Zero-divisors
  • Diameter
  • Girth
  • Path graph
  • Complete graph
  • Complete bipartite graph
  • Star graph

2010 Mathematics Subject Classification

  • 05C25
  • 05C75

References

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Cite this paper

APA

Sinha, D. & Kaur, B. (2019). On Beck’s zero-divisor graph. Notes on Number Theory and Discrete Mathematics, 25(4), 150-157, doi: 10.7546/nntdm.2019.25.4.150-157.

Chicago

Sinha, Deepa, and Bableen Kaur. “On Beck’s Zero-divisor Graph.” Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 150-157, doi: 10.7546/nntdm.2019.25.4.150-157.

MLA

Sinha, Deepa, and Bableen Kaur. “On Beck’s Zero-divisor Graph.” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 150-157. Print, doi: 10.7546/nntdm.2019.25.4.150-157.

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