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2 results

  • A Characterization of Bipartite Zero-divisor Graphs

  • Nader Jafari Rad, Sayyed Heidar Jafari
  • Journal:
    Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014
    Published online by Cambridge University Press:
    20 November 2018, pp. 188-193
    Print publication:
    14 March 2014
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  • In this paper we obtain a characterization for all bipartite zero-divisor graphs of commutative rings $R$ with 1 such that $R$ is finite or $\left| \text{Nil}\left( R \right) \right|\,\ne \,2$.

  • On Domination in Zero-Divisor Graphs

  • Nader Jafari Rad, Sayyed Heidar Jafari, Doost Ali Mojdeh
  • Journal:
    Canadian Mathematical Bulletin / Volume 56 / Issue 2 / 01 June 2013
    Published online by Cambridge University Press:
    20 November 2018, pp. 407-411
    Print publication:
    01 June 2013
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  • We first determine the domination number for the zero-divisor graph of the product of two commutative rings with 1. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a right zero-divisor.