Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE ZERO-DIVISOR GRAPHS OF ℤ(+)ℤn AND (ℤ(+)ℤn)[X]]

  • PARK, MIN JI (Department of Mathematics, College of Life Science and Nano Technology, Hannam University) ;
  • JEONG, JONG WON (School of Mathematics, Kyungpook National University) ;
  • LIM, JUNG WOOK (Department of Mathematics, College of Natural Sciences, Kyungpook National University) ;
  • BAE, JIN WON (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • Received : 2022.03.03
  • Accepted : 2022.04.28
  • Published : 2022.05.30
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Abstract

Let ℤ be the ring of integers and let ℤn be the ring of integers modulo n. Let ℤ(+)ℤn be the idealization of ℤn in ℤ and let (ℤ(+)ℤn)[X]] be either (ℤ(+)ℤn)[X] or (ℤ(+)ℤn)[[X]]. In this article, we study the zero-divisor graphs of ℤ(+)ℤn and (ℤ(+)ℤn)[X]]. More precisely, we completely characterize the diameter and the girth of the zero-divisor graphs of ℤ(+)ℤn and (ℤ(+)ℤn)[X]]. We also calculate the chromatic number of the zero-divisor graphs of ℤ(+)ℤn and (ℤ(+)ℤn)[X]].

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References

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