TY - JOUR
ID - 14423
TI - Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ \mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Pirzada, Shariefuddin
AU - Rather, Bilal
AU - Shaban, Rezwan Ul
AU - Chishti, Tariq
AD - Department of Mathematics, Hazratbal
AD - University of Kashmir
AD - Department of Mathematics, University of Kashmir
Y1 - 2023
PY - 2023
VL - 8
IS - 3
SP - 561
EP - 574
KW - Signless Laplacian matrix
KW - zero divisor graph, finite commutative ring, Eulers' s totient function
DO - 10.22049/cco.2022.27783.1353
N2 - 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