Representation of graphs zero divisores for rings.
Keywords:
Set zero divisor, zero dividers, algorithm
Abstract
The zero-divisor graph for a conmutative ring R, denoted by Γ(R), is a graph whose vertices are the elements of the set of divisor of zero, different of zero, on R. Two distinct vertices x and y are adyacentes in Γ(R) if and only if x•y = 0. In this work, they give some relevant results of the Γ(R) and also, an algorithm is presented for the representation of Γ(R) for rings of $\mathbb{Z}_{n}$.
References
Andersen, D. and Livinston, P. The zero divisor graph of a conmutative ring. J. Algebra, 217 (1999), 434-447.
Andersen, D. and Nasser, M. Becks Coloring of Conmutative ring. J. Algebra, 159 (1993), 500-514.
Beck, I. Coloring of Conmutative rings. J. Algebra, 116 (1988), 288-226.
Chartrand, G. and Lesniak, L. Graphs and Digraphs. Wadsworth and Brooks. 3era ed, California 1986.
Cordova, N.; Gholston, C. and Hauser, H. The Structure of Zero-Divisor Graphs. J. Algebra, 2005, prep print.
Fanelli, C. Grafo Divisor de Zero de un Anillo Conmutativo. Tesis de Mestría, Universidad de Maringa, Brazil, 2011.
Otero, J. Un Método matricial para el cálculo de las constantes de Davenport y Olson k-baricéntricas. Tesis de Maestría. Universidad de Oriente. Venezuela, 2011.
Rojo, A. Algebra I. Buenos Aires, Argentina, 1983.
Shuker, N.; Mohammad, H. and Ali, A. The Zero Divisor Graph of International Journal of Algebra, 6 (2012), 1049-1055.
Villarroel, F. La constante de olson k-baricéntrica y un teorema inverso de Erdös-Ginzburg-Ziv. Tesis Doctoral. Universidad Central de Venezuela, 2008.
Andersen, D. and Nasser, M. Becks Coloring of Conmutative ring. J. Algebra, 159 (1993), 500-514.
Beck, I. Coloring of Conmutative rings. J. Algebra, 116 (1988), 288-226.
Chartrand, G. and Lesniak, L. Graphs and Digraphs. Wadsworth and Brooks. 3era ed, California 1986.
Cordova, N.; Gholston, C. and Hauser, H. The Structure of Zero-Divisor Graphs. J. Algebra, 2005, prep print.
Fanelli, C. Grafo Divisor de Zero de un Anillo Conmutativo. Tesis de Mestría, Universidad de Maringa, Brazil, 2011.
Otero, J. Un Método matricial para el cálculo de las constantes de Davenport y Olson k-baricéntricas. Tesis de Maestría. Universidad de Oriente. Venezuela, 2011.
Rojo, A. Algebra I. Buenos Aires, Argentina, 1983.
Shuker, N.; Mohammad, H. and Ali, A. The Zero Divisor Graph of International Journal of Algebra, 6 (2012), 1049-1055.
Villarroel, F. La constante de olson k-baricéntrica y un teorema inverso de Erdös-Ginzburg-Ziv. Tesis Doctoral. Universidad Central de Venezuela, 2008.
Published
2018-12-29
How to Cite
Otero, J., Salazar, J., & Villarroel, F. (2018). Representation of graphs zero divisores for rings. Divulgaciones Matemáticas, 19(2), 44-51. Retrieved from https://produccioncientificaluz.org/index.php/divulgaciones/article/view/36611
Section
Research papers
