Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21288320230901Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ \mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $5615741442310.22049/cco.2022.27783.1353ENShariefuddin PirzadaDepartment of Mathematics, Hazratbal0000-0002-1137-517XBilal RatherUniversity of Kashmir0000-0003-1381-0291Rezwan Ul ShabanDepartment of Mathematics, University of KashmirTariq ChishtiUniversity of KashmirJournal Article20220427For 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