A note on annihilating ideal graph of zn

Department of Mathematics, DDE, Madurai Kamaraj University, India International Journal of Computer Science (IJCS Journal) Published by SK Research Group of Companies (SKRGC) Scholarly Peer Reviewed Research Journals

Format: Volume 6, Issue 1, No 03, 2018

Copyright: All Rights Reserved ©2018

Year of Publication: 2018

Author: N. Mohamed Rilwan, E. Chidambaram


View PDF Format


Let R be a commutative ring with identity etc...


[1] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434–447 (doi: 10.1006/jabr.1998.7840).

[2] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company, (1969).

[3] M. Axtell, N. Baeth and J. Stickles, Cut vertices in zero-divisor graph of finite commutative rings, Comm. Algebra, 39 (2011),2179–2188 (doi:10.1080/00927872.2010.488681)

[4] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings, I J. Algebra Appl., 10 (4) (2011), 727–739 (doi: 10.1142/S0219498811004896).

[5] M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings II, J. Algebra Appl., 10 (4) (2011), 741–753 (doi: 10.1142/S0219498811004902).

[6] G. Chartrand and L. Lesniak, Graphs and Digraphs Wadsworth and Brooks/ Cole, Monterey, CA, (1986).

[7] B. Cote, C. Ewing, M. Huhn, C. M. Plaut and D. Weber, Cut sets in zero-divisor graphs of finite commutative rings, Comm. Algebra, 39 (2011),2849–2861 (doi:10.1080/00927872.2010.489534).

[8] I. Kaplansky, Commutative Rings, rev. ed., University of Chicago Press Chicago(1974)

[9] S. P. Redmond, Central sets and radii of the zero-divisor graphs of commutative rings, Comm. Algebra, 34 (2006), 2389–2401 (doi:10.1080/00927870600649103).

[10] T. Tamizh Chelvam and K. Selvakumar, Central sets in the annihilating-ideal graph of commutative rings, J. Combin. Math. Combin. Comput. 88 (2014), 277–288.

[11] A. T. White, Graphs, Groups and Surfaces, North-Holland, Amsterdam,(1973).


claw-free graph, outer planar graph, unicyclic graph.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.   

Facebook IconYouTube IconTwitter IconVisit Our Blog