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On the zero-divisor graph of a commutative ring

Akbari, S ; Sharif University of Technology | 2004

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  1. Type of Document: Article
  2. DOI: 10.1016/S0021-8693(03)00435-6
  3. Publisher: Academic Press Inc , 2004
  4. Abstract:
  5. Let R be a commutative ring and Γ (R) be its zero-divisor graph. In this paper it is shown that for any finite commutative ring R, the edge chromatic number of Γ (R) is equal to the maximum degree of Γ (R), unless Γ (R) is a complete graph of odd order. In [D.F. Anderson, A. Frazier, A. Lauve, P.S. Livingston, in: Lecture Notes in Pure and Appl. Math., Vol. 220, Marcel Dekker, New York, 2001, pp. 61-72] it has been proved that if R and S are finite reduced rings which are not fields, then Γ (R) ≃ Γ (S) if and only if R ≃ S. Here we generalize this result and prove that if R is a finite reduced ring which is not isomorphic to ℤ2 × ℤ 2 or to ℤ6 and S is a ring such that Γ (R) ≃ Γ (S), then R ≃ S. © 2004 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Edge coloring ; Hamiltonian ; Zero-divisor graph
  8. Source: Journal of Algebra ; Volume 274, Issue 2 , 2004 , Pages 847-855 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0021869303004356