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Paper   IPM / M / 14180
School of Mathematics
  Title:   Classification of the toroidal Jacobson graphs
1.  H. R. Maimani
2.  M. R. Pournaki (Joint with H. Amraei and A. Zaeembashi)
  Status:   Published
  Journal: Bull. Malaysian Math. Soc.
  Year:  2015
  Pages:   DOI: 10.1007/s40840-015-0294-y
  Supported by:  IPM
Let R be a finite commutative ring with nonzero identity and denote its Jacobson radical by J(R). The Jacobson graph of R is the graph in which the vertex set is R\J(R), and two distinct vertices x and y are adjacent if and only if 1−xy is not a unit in R. In this paper, up to isomorphism, we classify the rings R whose Jacobson graphs are toroidal.

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