Geodesic
A Characterization of Bipartite Zero-divisor Graphs
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 188-193

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

In this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings $R$ with 1 such that $R$ is finite or $\left| \text{Nil}\left( R \right) \right|\,\ne \,2$ .
DOI : 10.4153/CMB-2013-011-6
Mots-clés : 13AXX, 05C25, zero-divisor graph, bipartite graph 
Rad, Nader Jafari; Jafari, Sayyed Heidar. A Characterization of Bipartite Zero-divisor Graphs. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 188-193. doi: 10.4153/CMB-2013-011-6
@article{10_4153_CMB_2013_011_6,
     author = {Rad, Nader Jafari and Jafari, Sayyed Heidar},
     title = {A {Characterization} of {Bipartite} {Zero-divisor} {Graphs}},
     journal = {Canadian mathematical bulletin},
     pages = {188--193},
     year = {2014},
     volume = {57},
     number = {1},
     doi = {10.4153/CMB-2013-011-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-011-6/}
}
TY  - JOUR
AU  - Rad, Nader Jafari
AU  - Jafari, Sayyed Heidar
TI  - A Characterization of Bipartite Zero-divisor Graphs
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 188
EP  - 193
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-011-6/
DO  - 10.4153/CMB-2013-011-6
ID  - 10_4153_CMB_2013_011_6
ER  - 
%0 Journal Article
%A Rad, Nader Jafari
%A Jafari, Sayyed Heidar
%T A Characterization of Bipartite Zero-divisor Graphs
%J Canadian mathematical bulletin
%D 2014
%P 188-193
%V 57
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2013-011-6/
%R 10.4153/CMB-2013-011-6
%F 10_4153_CMB_2013_011_6

[1] [1] Akbari, S. and Mohammadian, A., Zero-divisor graphs of non-commutative rings. J. Algebra 296 (2006), 462–479. Google Scholar | DOI

[2] [2] Akbari, S., Maimani, H. R., and Yassemi, S. When a zero-divisor graph is planar or a complete r-partitegraph. J. Algebra 270 (2003), 169–180. Google Scholar | DOI

[3] [3] Anderson, D. F., Frazier, A., Lauve, A., and Livingston, P. S., The zero-divisor graph of a commutativering, II. In: Ideal Theoretic Methods in Commutative Algebra (Columbia, MO, 1999), Dekker, New York, 2001, 61–72. Google Scholar

[4] [4] Anderson, D. F. and Livingston, P. S., The zero-divisor graph of a commutative ring. J. Algebra 217 (1999), 434–447. Google Scholar | DOI

[5] [5] Atiyah, M. F. and Macdonald, Ian G., Introduction to Commutative Algebra. Addison-Wesley Publishing Co, Reading, Mass.–London–Don Mills, Ont., 1969. Google Scholar

[6] [6] Dancheng, L. and Tongsuo, W., On bipartite zero-divisor graphs. Discrete Math. 309 (2009), 755–762. Google Scholar | DOI

[7] [7] DeMeyer, F. and Schneider, K., Automorphisms and zero divisor graphs of commutative rings. In: Commutative rings, Nova Sci. Publ., Hauppauge, NY, 2002, pp. 25–37. Google Scholar

[8] [8] Redmond, S. P., An ideal-based zero-divisor graph of a commutative ring. Comm. Algebra 31 (2003), 4425–4443. Google Scholar | DOI

[9] [9] Singh, S. and Zameeruddin, Q., Modern Algebra. Third reprint, Vikas Publishing House Pvt. Ltd., Dehli, 1995. Google Scholar

[10] [10] West, D. B., Introduction To Graph Theory. Prentice-Hall of India Pvt. Ltd, 2003. Google Scholar

Cité par Sources :