تقرير
Laplacian spectrum of weakly zero-divisor graph of the ring $\mathbb{Z}_{n}$
| العنوان: | Laplacian spectrum of weakly zero-divisor graph of the ring $\mathbb{Z}_{n}$ |
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| المؤلفون: | Shariq, Mohd, Mathil, Praveen, Kumar, Jitender |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Spectral Theory, 05C25, 05C50 |
| الوصف: | Let $R$ be a commutative ring with unity. The weakly zero-divisor graph $W\Gamma(R)$ of the ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$ and two vertices $x$, $y$ are adjacent if and only if there exists $r\in {\rm ann}(x)$ and $s \in {\rm ann}(y)$ such that $rs =0$. The zero-divisor graph of a ring is a spanning subgraph of the weakly zero-divisor graph. It is known that the zero-divisor graph of the ring $\mathbb{Z}_{{p^t}}$, where $p$ is a prime, is the Laplacian integral. In this paper, we obtain the Laplacian spectrum of the weakly zero-divisor graph $W\Gamma(\mathbb{Z}_{n})$ of the ring $\mathbb{Z}_{n}$ and show that $W\Gamma(\mathbb{Z}_{n})$ is Laplacian integral for arbitrary $n$. Comment: 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.12757 |
| رقم الأكسشن: | edsarx.2307.12757 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |