Signless Laplacian eigenvalues of the zero divisor graph associated to finite commutative ring $ mathbb{Z}_{p^{M_{1}}q^{M_{2}}} $
Author(s):
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
For a commutative ring $R$ with identity $1neq 0$, 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.
Keywords:
Language:
English
Published:
Communications in Combinatorics and Optimization, Volume:8 Issue: 3, Summer 2023
Pages:
561 to 574
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