International Journal of Nonlinear Analysis and Applications

Some of the graph energies of zero-divisor graphs of finite commutative rings

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

Abstract

 In this paper, we investigate some of the graph energies of the zero-divisor graph $\Gamma(R)$ of finite commutative rings $R$. Let $Z(R)$ be the set of zero-divisors of a commutative ring $R$ with non-zero identity and $Z^*(R)=Z(R)\setminus \{0\}$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set in $Z^*(R)$ and two vertices $u$ and $v$ are adjacent if and only if $uv=vu=0$. We investigate some energies of $\Gamma(R)$ for the commutative rings $R\simeq \mathbb{Z}_{p^2}\times \mathbb{Z}_{q}$, $R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}$ and $R\simeq \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}\times \mathbb{Z}_{p}$ where $p, q$ the prime numbers.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 7
July 2023
Pages 207-216
  • Receive Date: 12 March 2022
  • Revise Date: 05 August 2022
  • Accept Date: 13 September 2022