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

	Some of the graph energies of zero-divisor graphs of finite commutative rings
International Journal of Nonlinear Analysis and Applications
مقاله 19، دوره 14، شماره 7، مهر 2023، صفحه 207-216 اصل مقاله (362.61 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.7136
نویسندگان
Sharife Chokani؛ Fateme Movahedi^* ؛ Seyyed Mostafa Taheri
Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran
چکیده
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.
کلیدواژه‌ها
Commutative ring؛ Zero-divisor graph؛ Line graph؛ Minimum edge dominating energy؛ Laplacian energy
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