Geodesic
Description of finite nonnilpotent rings with planar zero-divisor graphs
Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 60-75

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The zero-divisor graph of an associative ring $R$ is a graph whose vertices are all nonzero (one-sided and two-sided) zero divisors of $R$, two distinct vertices $x,y$ are connected by an edge if and only if $xy=0$ or $yx=0$. In this paper, all finite nonnilpotent rings with planar zero-divisor graphs are completely described. In the previous paper by Kuzmina and Maltsev, the finite nilpotent rings with planar zero-divisor graphs were studied. Thus, this paper completes the description of finite rings with planar zero-divisor graphs. 
@article{DM_2009_21_4_a4,
     author = {A. S. Kuzmina},
     title = {Description of finite nonnilpotent rings with planar zero-divisor graphs},
     journal = {Diskretnaya Matematika},
     pages = {60--75},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2009_21_4_a4/}
}
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A. S. Kuzmina. Description of finite nonnilpotent rings with planar zero-divisor graphs. Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 60-75. http://geodesic.mathdoc.fr/item/DM_2009_21_4_a4/