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Characterizations of Three Classes of Zero-Divisor Graphs

Published online by Cambridge University Press:  20 November 2018

John D. LaGrange
John D. LaGrange*
Affiliation:
School of Natural Sciences, Indiana University Southeast, New Albany, Indiana 47150, USA e-mail: lagrangej@lindsey.edu
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Abstract

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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.

Keywords

13A9913M99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 1 , 01 March 2012 , pp. 127 - 137
Copyright
Copyright © Canadian Mathematical Society 2012

References

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