On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
| Autor: | S. Pirzada, B.A. Rather, T.A. Chishti |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 13, Iss 1, Pp 48-57 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2075-9827 2313-0210 |
| DOI: | 10.15330/cmp.13.1.48-57 |
| Popis: | For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and only if $xy=0$. We find the distance Laplacian spectrum of the zero divisor graphs $\Gamma(\mathbb{Z}_{n})$ for different values of $n$. Also, we obtain the distance Laplacian spectrum of $\Gamma(\mathbb{Z}_{n})$ for $n=p^z$, $z\geq 2$, in terms of the Laplacian spectrum. As a consequence, we determine those $n$ for which zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is distance Laplacian integral. |
| Databáze: | Directory of Open Access Journals |
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