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Zero-divisor Graphs of Partially Ordered Sets

Kamali Andani, Ali Akbar | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44706 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Pournaki, Mohammad Reza
  7. Abstract:
  8. Let (P;≼) be a partially ordered set (poset, briefly) with a least element 0. In this thesis, we deal with zero-divisor graphs of posets. We show that if the chromatic number r(P) and the clique number r(P) (x(r(P)) and !(r(P)), respectively) are finite, then x(r(P)) = !(w(P)) = n in which n is the number of minimal prime ideals of P. We also prove that the diameter of such a graph is either 1, 2 or 3 while its girth is either 3, 4 or 1
  9. Keywords:
  10. Graph Coloring ; Chromatic Number ; Clique Number ; Graph Diameter ; Annihilator ; Quasiordered Sets ; Ideal ; Girth Graph

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