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Unit graphs associated with rings

Ashrafi, N ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1080/00927870903095574
  3. Publisher: 2010
  4. Abstract:
  5. 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. (These terms are defined in Definitions and Remarks 4.1, 5.1, 5.3, 5.9, and 5.13.)
  6. Keywords:
  7. Chromatic index ; Connectedness ; Diameter ; Girth ; Planarity ; Unit graph
  8. Source: Communications in Algebra ; Volume 38, Issue 8 , 2010 , Pages 2851-2871 ; 00927872 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/00927870903095574