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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1211, author = {S. Ebrahimi Atani and M. Shajari Kohan and Z. Ebrahimi Sarvandi}, title = {An ideal-based zero-divisor graph of direct products of commutative rings}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {34}, year = {2014}, pages = {45-53}, zbl = {1313.16095}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1211} }
S. Ebrahimi Atani; M. Shajari Kohan; Z. Ebrahimi Sarvandi. An ideal-based zero-divisor graph of direct products of commutative rings. Discussiones Mathematicae - General Algebra and Applications, Tome 34 (2014) pp. 45-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1211/
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