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Paper   IPM / M / 11142
School of Mathematics
  Title:   Unit graphs associated with rings
1.  H. R. Maimani
2.  M. R. Pournaki (Joint with N. Ashrafi and S. Yassemi)
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  38
  Year:  2010
  Pages:   2851-2871
  Supported by:  IPM
Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x+y is a unit of R. In this article, the basic properties of G(R) are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity of G(R) are given.

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