A variation of zero-divisor graphs

Raibatak Sen Gupta; M.K. Sen; Shamik Ghosh

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 2, page 159-176
  • ISSN: 1509-9415

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Raibatak Sen Gupta, M.K. Sen, and Shamik Ghosh. "A variation of zero-divisor graphs." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 159-176. <http://eudml.org/doc/276462>.

@article{RaibatakSenGupta2015,
abstract = {},
author = {Raibatak Sen Gupta, M.K. Sen, Shamik Ghosh},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {rings; zero-divisor graphs; finite fields; coding sequence of a graph; polynomial representation of a graph},
language = {eng},
number = {2},
pages = {159-176},
title = {A variation of zero-divisor graphs},
url = {http://eudml.org/doc/276462},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Raibatak Sen Gupta
AU - M.K. Sen
AU - Shamik Ghosh
TI - A variation of zero-divisor graphs
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 2
SP - 159
EP - 176
AB -
LA - eng
KW - rings; zero-divisor graphs; finite fields; coding sequence of a graph; polynomial representation of a graph
UR - http://eudml.org/doc/276462
ER -

References

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  2. [2] D.F. Anderson, M.C. Axtell and J.A. Stickles Jr., Zero-divisor graphs in commutative rings, Commutative Algebra: Noetherian and Non-Noetherian Perspectives (2011), 23-45. doi: 10.1007/978-1-4419-6990-3_2 
  3. [3] D.F. Anderson and P. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434-447. doi: 10.1006/jabr.1998.7840 
  4. [4] D.F. Anderson, A. Frazier, A. Lauve and P.S. Livingston, The zero-divisor graph of a commutative ring II, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York 220 (2001), 61-72. Zbl1035.13004
  5. [5] N. Ashrafi, H.R. Maimani, M.R. Pournaki and S. Yassemi, Unit graphs associated with rings, Comm. Algebra 38 (2010), 2851-2871. doi: 10.1080/00927870903095574 Zbl1219.05150
  6. [6] S.E. Atani, M.S. Kohan and Z.E. Sarvandi, An ideal-based zero-divisor graph of direct products of commutative rings, Discuss. Math. Gen. Algebra Appl. 34 (2014), 45-53. doi: 10.7151/dmgaa.1211 Zbl1301.05163
  7. [7] M. Axtell, J. Stickles and W. Trampbachls, Zero-divisor ideals and realizable zero-divisor graphs, Involve 2 (2009), 17-27. doi: 10.2140/involve.2009.2.17 Zbl1169.13301
  8. [8] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208-226. doi: 10.1016/0021-8693(88)90202-5 
  9. [9] I. Bozic and Z. Petrovic, Zero-divisor graphs of matrices over commutative rings, Comm. Algebra 37 (2009), 1186-1192. doi: 10.1080/00927870802465951 Zbl1185.16031
  10. [10] N. Ganesan, Properties of rings with a finite number of zero divisors, Math. Annalen 157 (3) (1964), 215-218. doi: 10.1007/BF01362435 Zbl0135.07704
  11. [11] S. Redmond, The zero-divisor graph of a non-commutative ring, International Journal of Commutative Rings 1 (4) (2002), 203-211. Zbl1195.16038
  12. [12] D.B. West, Introduction to Graph Theory (Prentice Hall of India New Delhi, 2003). 

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