The Zero-divisor Graph of Zn [X ]

Min Ji Park; Eun Sup Kim; Jung Wook Lim

doi:10.5666/KMJ.2020.60.4.723

The Zero-divisor Graph of Z_n [X ]

Min Ji Park
, Eun Sup Kim
, Jung Wook Lim

Hannam University
Kyungpook National University

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	723-729
Number of pages	7
Journal	Kyungpook Mathematical Journal
Volume	60
Issue number	4
DOIs	https://doi.org/10.5666/KMJ.2020.60.4.723
State	Published - 2020

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10.5666/KMJ.2020.60.4.723

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title = "The Zero-divisor Graph of Zn [X ]",

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

author = "Park, \{Min Ji\} and Kim, \{Eun Sup\} and Lim, \{Jung Wook\}",

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T1 - The Zero-divisor Graph of Zn [X ]

AU - Park, Min Ji

AU - Kim, Eun Sup

AU - Lim, Jung Wook

PY - 2020

Y1 - 2020

N2 - Let Zn be the ring of integers modulo n and let Zn[X] be either Zn[X] or Zn[X]|. Let r(Zn[X]) be the zero-divisor graph of Zn[X]|. In this paper, we study some properties of r(Zn[X]). More precisely, we completely characterize the diameter and the girth of r(Zn[X]|). We also calculate the chromatic number of r(Zn[X]|).

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

UR - https://www.scopus.com/pages/publications/85099438381

U2 - 10.5666/KMJ.2020.60.4.723

DO - 10.5666/KMJ.2020.60.4.723

M3 - Article

AN - SCOPUS:85099438381

SN - 1225-6951

VL - 60

SP - 723

EP - 729

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

IS - 4

ER -

The Zero-divisor Graph of Z_n [X ]

Abstract

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