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ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY

  • SLAVKO M. MOCONJA (a1) and ZORAN Z. PETROVIĆ (a2)

Abstract

In this paper we investigate the center, radius and girth of comaximal graphs of commutative rings. We also provide some counterexamples to the results concerning the relation between isomorphisms of comaximal graphs and the rings in question. In addition, we investigate the relation between the comaximal graph of a ring and its subrings of a certain type.

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Copyright

Corresponding author

For correspondence; e-mail: slavko@matf.bg.ac.rs

Footnotes

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This work was partially supported by Ministry of Science and Environmental Protection of Republic of Serbia Project #144018 and Project #144020.

Footnotes

References

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[1]Atiyah, M. F. and Macdonald, I. G., Introduction to Commutative Algebra (Addison-Wesley, Reading, MA, 1969).
[2]Beck, I., ‘Coloring of commutative rings’, J. Algebra 116 (1988), 208226.
[3]Maimani, H. R., Salimi, M., Sattari, A. and Yassemi, S., ‘Comaximal graph of commutative rings’, J. Algebra 319 (2008), 18011808.
[4]Nikiforov, V., ‘Graphs with many copies of a given subgraph’, Electron. J. Combin. 15(1) (2008), # N6.
[5]Petrović, Z. Z. and Moconja, S. M., ‘On graphs associated to rings’, Novi Sad J. Math. 38(3) (2008), 3338.
[6]Redmond, S., ‘The zero-divisor graph of a non-commutative ring’, Internat. J. Commutative Rings 1(4) (2002), 203211.
[7]Sharma, P. D. and Bhatwadekar, S. M., ‘A note on graphical representation of rings’, J. Algebra 176 (1995), 124127.
[8]Szigeti, J. and van Wyk, L., ‘Subrings which are closed with respect to taking the inverse’, J. Algebra 318 (2007), 10681076.
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ON THE STRUCTURE OF COMAXIMAL GRAPHS OF COMMUTATIVE RINGS WITH IDENTITY

  • SLAVKO M. MOCONJA (a1) and ZORAN Z. PETROVIĆ (a2)

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