Geodesic
Some Results on the Domination Number of a Zero-divisor Graph
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 573-578

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we investigate the domination, total domination, and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of $\Gamma \left( {R}/{I}\; \right)$ and ${{\Gamma }_{1}}\left( R \right)$ , and the domination numbers of $\Gamma \left( R \right)$ and $\Gamma \left( R\left[ x,\,\alpha ,\,\delta\right] \right)$ , where $R\left[ x,\,\alpha ,\,\delta\right]$ is the Ore extension of $R$ , are studied.
DOI : 10.4153/CMB-2014-027-8
Mots-clés : 05C75, 13H10, zero-divisor graph, domination number 
Kiani, Sima; Maimani, Hamid Reza; Nikandish, Reza. Some Results on the Domination Number of a Zero-divisor Graph. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 573-578. doi: 10.4153/CMB-2014-027-8
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[1] [1] Afkhami, M., Khashyarmanesh, K., and Khorsandi, M. R., Zero-divisor graphs of Ore extension rings. J. Algebra Appl. 10 (2011), no. 6, 1309–1317. Google Scholar | DOI

[2] [2] Anderson, D. F. and Livingston, P. S., The zero-divisor graph of a commutative ring. J. Algebra 217 (1999), no. 2, 434–447. Google Scholar | DOI

[3] [3] Annin, S., Associated primes over Ore extension rings. J. Algebra Appl. 3 (2004), no. 2, 193–205. Google Scholar | DOI

[4] [4] Beck, I., Coloring of commutative rings. J. Algebra 116 (1988), no. 1, 208–226. Google Scholar | DOI

[5] [5] Jafari, N. Rad, Jafari, S. H., and Mojdeh, D. A., On domination in zero-divisor graphs. Canad. Math. Bull. 56 (2013), no. 2, 407–411. Google Scholar | DOI

[6] [6] Maimani, H. R., Pournaki, M. R., Tehranian, A., and Yassemi, S., Graphs attached to rings revisited. Arab. J. Sci. Eng. 36 (2011), no. 6, 997–1011. Google Scholar | DOI

[7] [7] Maimani, H. R., Pournaki, M. R., and Yassemi, S., Zero-divisor graph with respect to an ideal. Comm. Algebra 34 (2006), no. 3, 923–929. Google Scholar | DOI

[8] [8] Mojdeh, D. A. and Rahimi, A. M., Dominating sets of some graphs associated to commutative rings. Comm. Algebra 40 (2012), no. 9, 3389–3396. Google Scholar | DOI

[9] [9] Nielsen, P. P., Semi-commutativity and the McCoy condition. J. Algebra 298 (2006), no. 1, 134–141. Google Scholar | DOI

[10] [10] Redmond, S. P., An ideal-based zero-divisor graph of a commutative ring. Comm. Algebra 31 (2003), no. 9, 4425–4443. Google Scholar | DOI

[11] [11] Sharp, R. Y., Steps in commutative algebra. London Mathematical Society Student Texts, 19, Cambridge University Press, Cambridge, 1990. Google Scholar

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