Geodesic
Finite rings with some restrictions on zero-divisor graphs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 48-59

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The zero-divisor graph $\Gamma(R)$ of an associative ring $R$ is the graph whose vertices are all nonzero zero-divisors (one-sided and two-sided) of $R$, and two distinct vertices $x$ and $y$ are joined by an edge if and only if either $xy=0$ or $yx=0$. In the present paper, we give full description of finite rings with regular zero-divisor graphs. We also prove some properties of finite rings such that their zero-divisor graphs satisfy the Dirac condition.
Keywords: zero-divisor graph, regular graph, associative ring, finite ring. 
@article{IVM_2014_12_a4,
     author = {A. S. Kuzmina and Yu. N. Maltsev},
     title = {Finite rings with some restrictions on zero-divisor graphs},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--59},
     publisher = {mathdoc},
     number = {12},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_12_a4/}
}
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A. S. Kuzmina; Yu. N. Maltsev. Finite rings with some restrictions on zero-divisor graphs. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2014), pp. 48-59. http://geodesic.mathdoc.fr/item/IVM_2014_12_a4/