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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## Details

### 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

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## Related papers

## Cite this paper

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.