Geodesic
Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs
Algebra i logika, Tome 52 (2013) no. 2, pp. 203-218

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The zero-divisor graph of an associative ring $R$ is a graph such that its vertices are all nonzero (one-sided and two-sided) zero-divisors, and moreover, two distinct vertices $x$ and $y$ are joined by an edge iff $xy=0$ or $yx=0$. We give a complete description of varieties of associative rings in which all finite rings have Hamiltonian zero-divisor graphs. Also finite decomposable rings with unity having Hamiltonian zero-divisor graphs are characterized.
Keywords: zero-divisor graph, Hamiltonian graph, variety of associative rings, finite ring. 
@article{AL_2013_52_2_a4,
     author = {Yu. N. Mal'tsev and A. S. Kuz'mina},
     title = {Describing ring varieties in which all finite rings have {Hamiltonian} zero-divisor graphs},
     journal = {Algebra i logika},
     pages = {203--218},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_2_a4/}
}
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Yu. N. Mal'tsev; A. S. Kuz'mina. Describing ring varieties in which all finite rings have Hamiltonian zero-divisor graphs. Algebra i logika, Tome 52 (2013) no. 2, pp. 203-218. http://geodesic.mathdoc.fr/item/AL_2013_52_2_a4/