Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Zero-divisor Graph of ℤn[X]]

  • Park, Min Ji (Department of Mathematics, College of Life Science and Nano Technology, Hannam University) ;
  • Kim, Eun Sup (Department of Mathematics, College of Natural Sciences, Kyungpook National University) ;
  • Lim, Jung Wook (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • Received : 2020.06.13
  • Accepted : 2020.08.04
  • Published : 2020.12.31
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Abstract

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

Keywords

Acknowledgement

We would like to thank the referee for several valuable suggestions.

References

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