On distance Laplacian spectrum of zero divisor graphs of the ring $\mathbb{Z}_{n}$
2021 ◽
Vol 13
(1)
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pp. 48-57
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Keyword(s):
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.
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2007 ◽
Vol 2007
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pp. 1-15
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2020 ◽
Vol 12
(1)
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pp. 84-101
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2016 ◽
Vol 16
(07)
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pp. 1750132
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2015 ◽
Vol 14
(06)
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pp. 1550079
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2019 ◽
Vol 19
(12)
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pp. 2050226
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2019 ◽
Vol 19
(08)
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pp. 2050155
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2018 ◽
Vol 17
(07)
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pp. 1850121
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