On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
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 Laplacia...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-03-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4143 |
| _version_ | 1797205802084204544 |
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| author | S. Pirzada B.A. Rather T.A. Chishti |
| author_facet | S. Pirzada B.A. Rather T.A. Chishti |
| author_sort | S. Pirzada |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T08:56:54Z |
| format | Article |
| id | doaj.art-ad8f11e48c1b4e798612407513c6d4d5 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:54Z |
| publishDate | 2021-03-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-ad8f11e48c1b4e798612407513c6d4d52024-04-16T07:05:54ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102021-03-01131485710.15330/cmp.13.1.48-573617On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$S. Pirzada0B.A. Rather1https://orcid.org/0000-0003-1381-0291T.A. Chishti2University of Kashmir, 190006, Srinagar, Kashmir, IndiaUniversity of Kashmir, 190006, Srinagar, IndiaUniversity of Kashmir, 190006, Srinagar, IndiaFor 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.https://journals.pnu.edu.ua/index.php/cmp/article/view/4143laplacian matrixdistance laplacian matrixcommutative ringzero divisor graph |
| spellingShingle | S. Pirzada B.A. Rather T.A. Chishti On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ Karpatsʹkì Matematičnì Publìkacìï laplacian matrix distance laplacian matrix commutative ring zero divisor graph |
| title | On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ |
| title_full | On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ |
| title_fullStr | On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ |
| title_full_unstemmed | On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ |
| title_short | On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$ |
| title_sort | on distance laplacian spectrum of zero divisor graphs of the ring mathbb z n |
| topic | laplacian matrix distance laplacian matrix commutative ring zero divisor graph |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/4143 |
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