Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 8 3 2023 09 01 Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ \mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $ 561 574 14423 10.22049/cco.2022.27783.1353 EN Shariefuddin Pirzada Department of Mathematics, Hazratbal Bilal Rather University of Kashmir Rezwan Ul Shaban Department of Mathematics, University of Kashmir Tariq Chishti University of Kashmir Journal Article 2022 04 27 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. https://comb-opt.azaruniv.ac.ir/article_14423_bb4de937deddf13539bf65ceb1ee53d4.pdf