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# Characterizations of Three Classes of Zero-Divisor Graphs

Published:2011-05-30
Printed: Mar 2012
• John D. LaGrange,
School of Natural Sciences, Indiana University Southeast, New Albany, Indiana 47150, USA
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## Abstract

The zero-divisor graph $\Gamma(R)$ of a commutative ring $R$ is the graph whose vertices consist of the nonzero zero-divisors of $R$ such that distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$. In this paper, a characterization is provided for zero-divisor graphs of Boolean rings. Also, commutative rings $R$ such that $\Gamma(R)$ is isomorphic to the zero-divisor graph of a direct product of integral domains are classified, as well as those whose zero-divisor graphs are central vertex complete.
 MSC Classifications: 13A99 - None of the above, but in this section 13M99 - None of the above, but in this section

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