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Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ \mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 8، شماره 3، آذر 2023، صفحه 561-574 اصل مقاله (434.15 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27783.1353 | ||
| نویسندگان | ||
| Shariefuddin Pirzada* 1؛ Bilal Rather2؛ Rezwan Ul Shaban3؛ Tariq Chishti2 | ||
| 1Department of Mathematics, Hazratbal | ||
| 2University of Kashmir | ||
| 3Department of Mathematics, University of Kashmir | ||
| چکیده | ||
| For a commutative ring $R$ with identity $1\neq 0$, let the set $Z(R)$ denote the set of zero-ivisors and let $Z^{*}(R)=Z(R)\setminus \{0\}$ be the set of non-zero zero-divisors of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set is $Z^{*} (R)$ and two vertices $u, v \in Z^*(R)$ are adjacent if and only if $uv=vu=0$. In this article, we find the signless Laplacian spectrum of the zero divisor graphs $ \Gamma(\mathbb{Z}_{n}) $ for $ n=p^{M_{1}}q^{M_{2}}$, where $ p<q $ are primes and $ M_{1} , M_{2} $ are positive integers. | ||
| کلیدواژهها | ||
| Signless Laplacian matrix؛ zero divisor graph, finite commutative ring, Eulers' s totient function | ||
| مراجع | ||
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