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Paper   IPM / M / 14163
School of Mathematics
  Title:   The nonorientable genus of some Jacobson graphs and classification of the projective ones
  Author(s): 
1.  H. R. Maimani
2.  M. R. Pournaki (Joint with H. Amraei and A. Zaeembashi)
  Status:   Published
  Journal: Publ. Math. Debrecen
  Vol.:  88
  Year:  2016
  Pages:   425-437
  Supported by:  IPM
  Abstract:
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, the nonorientable genus of some Jacobson graphs is either computed or estimated by a lower bound. As an application, the rings R with projective Jacobson graphs are classified.


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