Geodesic
An ideal-based zero-divisor graph of direct products of commutative rings
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 45-53

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In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings.
Keywords: zero-divisor graph, ideal-based, diameter, girth, finite direct product 
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Atani, S.; Kohan, M.; Sarvandi, Z. An ideal-based zero-divisor graph of direct products of commutative rings. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 45-53. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a2/