논문KCI 등재
The Zero-divisor Graph of Zn[X]]
경북대학교 자연과학대학 수학과|2020.12|Kyungpook Mathematical Journal|제60권 제4호|pp. 723-729|DOI 10.5666/KMJ.2020.60.4.723
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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]]).
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]]).
참고문헌 (9)
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- I. Beck, "Coloring of commutative rings", J. Algebra, 116, pp.208~226 (1988)
- D. E. Fields, "Zero divisors and nilpotent elements in power series rings", Proc. Amer. Math. Soc., 27, pp.427~433 (1971)
- S. Mulay, "Cycles and symmetries of zero-divisors", Comm. Algebra, 30, pp.3533~3558 (2002)
- 피승준, "The Zero-divisor Graph of the Ring of Integers Modulo n", Kyungpook Mathematical Journal, 59(4), pp.591~601 (2019), 경북대학교 자연과학대학 수학과[DOI]
관련 논문AI추천
Chromatic number of the zero-divisor graphs over modulesRezvan Varmazyar, Sang Cheol Lee대한수학회 · 대한수학회논문집2019 · 제34권 제2호The Zero-divisor Graph of the Ring of Integers Modulo n김세훈, 임정욱, 피승준경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제4호Some graph theoretical properties over zero-divisor graphs of special finite commutative ringsM. Togan, N. Akgunes장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제2호Extended zero-divisor graphs of idealizationsDriss Bennis, Fouad Taraza, Jilali Mikram대한수학회 · 대한수학회논문집2017 · 제32권 제1호An Ideal-based Extended Zero-divisor Graph on RingsMohammad Ashraf, Mohit Kumar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제3호On the Diameter, Girth and Coloring of the Strong Zero‑Divisor Graph of Near‑ringsProhelika Das경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제4호
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