Kyungpook Mathematical Journal

  • 제59권4호
  • /
  • Pages.591-601
  • /
  • 2019
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The Zero-divisor Graph of the Ring of Integers Modulo n

  • Pi, Seung Jun (Department of Mathematics, College of Natural Sciences, Kyungpook National University) ;
  • Kim, Se Hun (Department of Mathematics, Seoul National University) ;
  • Lim, Jung Wook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • 투고 : 2018.10.15
  • 심사 : 2019.11.11
  • 발행 : 2019.12.23
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초록

Let ℤn be the ring of integers modulo n and Γ(ℤn) the zero-divisor graph of ℤn. In this paper, we study some properties of Γ(ℤn). More precisely, we completely characterize the diameter and the girth of Γ(ℤn). We also calculate the chromatic number of Γ(ℤn).

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참고문헌

  1. D. F. Anderson, M. C. Axtell, and J. A. Stickles, Jr, Zero-divisor graphs in commutative rings, Commutative Algebra: Noetherian and Non-Noetherian Perspectives, 23-45, Springer, New York, 2011.
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  5. S. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra, 30(2002), 3533-3558. https://doi.org/10.1081/AGB-120004502