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Results on annihilator graph of a commutative Ring

International Conference on Algebra and Discrete Mathematics (ICADM-2020) on 24 to 26, June 2020, Department of Mathematics, DDE, Madurai Kamaraj University, Tamil Nadu, India. International Journal of Computer Science (IJCS) Published by SK Research Group of Companies (SKRGC)

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Abstract

Let R be a commutative ring with identity 1. Z(R) be its set of zero-divisors, and if a .... Download PDF...

References

[1] Anderson, D. F., Livinston, P.S. (1999). The zero divisor graph of a commutative ring. J. Algebra 217: 434-447.

[2] Anderson, D. F., Mulay, S.B. (2007). On the diameter and girth of a zerodivisor graph. J. Pure Appl. Algebra 210(2): 543-550

[3] A. Badawi, On the annihilator graph of a commutative ring, Comm. Algebra 42 (2014), no. 1, 108121.

[4] Lucas, T. G. (2006). The diameter of a zero-divisor graph. J. Algebra 301: 3533-3558..

[5] Anderson, D. F. (2008). On the diameter and girth of a zero divisior graph, (2). Houston J. Math. 34: 361-371.

[6] H. Matsumura, Commutative Ring Theory (Cambridge University Press,1986).

[7] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra (Addison-Wesly, 1969).

[8] N. Ganesan, Properties of rings with a finite number of zero divisors, Math. Ann 157(1964)215-218.

[9] R. Y. Sharp, Steps in Commutative Algebra (Cambridge University Press,1990).

[10] I. Beck, coloring of commutative rings, J. Algebra 116 (1988) 208-226.

[11] T. Tamizh Chelvam and K. Selvakumar, On the genus of the annihilator graph of a commutative ring,Algebra and Discrete Mathematics Volume 24 (2017). Number 2, pp. 191208.

[12] Beck, I. (1988). Coloring of commutative rings. J. Algebra 116:208-226.

[13] Akbari, S., Maimani, H.R., Yassemi, S.(2003). When a zero divisor graph is planar or a complete r-partite graph. J. Algebra 270:169-180.

[14] Bollaboas , B. (1998). Modern Graph Theory. New York: Springer-Verlag.

Keywords

Annihilator Graph; diameter; girth; Zero divisor Graph

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  • Format Volume 8, Issue 2, No 4, 2020.
  • Copyright All Rights Reserved ©2020
  • Year of Publication 2020
  • Author A.M.ANTO, T.SUMI, B.UMA DEVI
  • Reference IJCS-374
  • Page No 2537-2544

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