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Graphs attached to rings revisited

Maimani, H. R ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s13369-011-0096-y
  3. Abstract:
  4. In this paper, we discuss some recent results on graphs attached to rings. In particular, we deal with comaximal graphs, unit graphs, and total graphs. We then define the notion of cototal graph and, using this graph, we characterize the rings which are additively generated by their zero divisors. Finally, we glance at graphs attached to other algebraic structures
  5. Keywords:
  6. Chromatic index ; Chromatic number ; Clique number ; Comaximal graph ; Connectedness ; Cototal graph ; Counit graph ; Diameter ; Finite ring ; Girth ; Hamiltonian cycle ; Hamiltonian graph ; Planarity ; Total graph ; Unit element ; Unit graph ; Weakly perfect graph ; Zero-divisor graph
  7. Source: Arabian Journal for Science and Engineering ; Volume 36, Issue 6 , 2011 , Pages 997-1011 ; 13198025 (ISSN)
  8. URL: http://link.springer.com/article/10.1007/s13369-011-0096-y#page-1