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Paper   IPM / M / 13514
School of Mathematics
  Title:   Classification of rings with unit graphs having domination number less than four
1.  H. R. Maimani
2.  M. R. Pournaki
3.  S. Yassemi (Joint with S. Kiani)
  Status:   Published
  Journal: Rend. Sem. Math. Univ. Padova
  Vol.:  133
  Year:  2015
  Pages:   173-195
  Supported by:  IPM
Let R be a finite commutative ring with nonzero identity. The unit graph of R is the graph obtained by setting all the elements of R to be the vertices and defining distinct vertices x and y to be adjacent if and only if x+y is a unit element of R. In this paper, a classification of finite commutative rings with nonzero identity in which their unit graphs have domination number less than four is given.

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