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/}
}
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/