سلام
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{\centering \textbf{Abstract}\vskip1ex}
The concept of zero divisor graph of a ring was introduced by Beck in his study
on the coloring problem of a commutative ring \cite{2}.
He considered a ring $R$ as the vertex set of a graph $G(R)$.
Two distinct vertices $x$ and $y$ of $G(R)$ are defined to be adjacent
if and only if $xy = 0$. Anderson and Livingston \cite{1},
considered the set of all non-zero zero divisors as the vertex set to
simplify the Beck's zero divisor graph. The edges can be defined in a similar
way as Beck's seminal paper. This graph is denoted by $\Gamma(R)$.
In this paper we use the Anderson-Livingston's definition of zero
devisor graph and
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© 2022 University
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\textbf{Keywords:}\\[1ex]
{\footnotesize Text,\\ Other,\\ Some,\\ Example}
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\textbf{AMS Subject Classification (2020):}\\[1ex]
{\footnotesize 05C50; 94B05; 05B05}
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\textbf{Article History:}\\[1ex]
{\footnotesize Received: 07 August 2022,\\ Accepted: 11 November 2022,}
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