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Paper   IPM / M / 11523
School of Mathematics
  Title:   On zero-divisor graphs of boolean rings
  Author(s):  Ali Mohammadian
  Status:   Published
  Journal: Pacific J. Math.
  Vol.:  251
  Year:  2011
  Pages:   375-383
  Supported by:  IPM
The zero-divisor graph of ring R is the graph whose vertices consist of the non-zero zero-divisors of R in which two distinct vertices a and b are adjacent if and only if either ab=0 or ba=0. In this paper, we investigate some properties of zero-divisor graphs of Boolean rings. Among other results, we prove that for any two rings R and S with Γ(R) ≅ Γ(S), if R is Boolean and |R| > 4, then RS.

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