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Finite rings with complete bipartite zero-divisor graphs

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Abstract

We describe all finite associative rings with complete bipartite zero-divisor graphs.

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References

  1. I. Beck, “Coloring of Commutative Rings,” J. Algebra 116(1), 208–226 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  2. D. F. Anderson and P. S. Livingston, “The Zero-Divisor Graph of a Commutative Ring,” J. Algebra 217(2), 434–447 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Akbari and A. Mohammadian, “On Zero-Divisor Graphs of Finite Rings,” J. Algebra 314(1), 168–184 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Akbari, H. R. Maimani, and S. Yassemi, “When Zero-Divisor Graph is Planar or a Complete r-Partite Graph,” J. Algebra 270(1), 169–180 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Belshoff and J. Chapman, “Planar Zero-Divisor Graphs,” J. Algebra 316(1), 471–480 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. S. Kuz’mina and Yu. N. Maltsev, “Nilpotent Finite Rings with Planar Zero-Divisor Graphs,” Asian-European J. Math. 1(4), 565–574 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. S. Kuz’mina, “Description of Finite Nilpotent Rings with Planar Zero-Divisor Graphs,” Diskretn. Mat. 4, 60–75 (2009).

    MathSciNet  Google Scholar 

  8. A. S. Kuz’mina, “On Structure of Rings with Planar Zero-Divisor Graphs,” Izv. Altaisk. Gos. Univ. 1, 17–26 (2009).

    Google Scholar 

  9. B. Bollobas, Graph Theory: An Introductory Course. Graduate Texts in Mathematics (Springer-Verlag, New York-Heidelberg-Berlin, 1979), Vol. 63.

    MATH  Google Scholar 

  10. V. P. Elizarov, Finite Rings (Gelios ARV, Moscow, 2006) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Altai State Pedagogical Academy, ul. Molodezhnaya 55, Barnaul, 656031, Russia

    A. S. Kuzmina & Yu. N. Maltsev

Authors
  1. A. S. Kuzmina
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  2. Yu. N. Maltsev
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Corresponding author

Correspondence to A. S. Kuzmina.

Additional information

Original Russian Text © A.S. Kuzmina and Yu.N. Maltsev, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 3, pp. 24–30.

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Kuzmina, A.S., Maltsev, Y.N. Finite rings with complete bipartite zero-divisor graphs. Russ Math. 56, 20–25 (2012). https://doi.org/10.3103/S1066369X12030048

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  • DOI: https://doi.org/10.3103/S1066369X12030048

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