Geodesic
Characterizations of Three Classes of Zero-Divisor Graphs
Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 127-137

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DOI

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.
DOI : 10.4153/CMB-2011-107-3
Mots-clés : 13A99, 13M99 
LaGrange, John D. Characterizations of Three Classes of Zero-Divisor Graphs. Canadian mathematical bulletin, Tome 55 (2012) no. 1, pp. 127-137. doi: 10.4153/CMB-2011-107-3
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     title = {Characterizations of {Three} {Classes} of {Zero-Divisor} {Graphs}},
     journal = {Canadian mathematical bulletin},
     pages = {127--137},
     year = {2012},
     volume = {55},
     number = {1},
     doi = {10.4153/CMB-2011-107-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-107-3/}
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