THE ZERO-DIVISOR GRAPHS OF Z(+)Zn AND (Z(+)Zn )[X ]

Min Ji Park; Jong Won Jeong; Jung Wook Lim; Jin Won Bae

doi:10.14317/jami.2022.729

THE ZERO-DIVISOR GRAPHS OF Z(+)Z_n AND (Z(+)Z_n )[X ]

Min Ji Park, Jong Won Jeong, Jung Wook Lim, Jin Won Bae

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

Abstract

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

Original language	English
Pages (from-to)	729-740
Number of pages	12
Journal	Journal of Applied Mathematics and Informatics
Volume	40
Issue number	3-4
DOIs	https://doi.org/10.14317/jami.2022.729
State	Published - 2022

Keywords

chromatic number
clique
diameter
girth
Γ((Z(+)Z)[X]])
Γ(Z(+)Z)

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10.14317/jami.2022.729

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title = "THE ZERO-DIVISOR GRAPHS OF Z(+)Zn AND (Z(+)Zn )[X ]",

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 zerodivisor 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 zerodivisor graphs of Z(+)Zn and (Z(+)Zn)[X]].",

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author = "Park, {Min Ji} and Jeong, {Jong Won} and Lim, {Jung Wook} and Bae, {Jin Won}",

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doi = "10.14317/jami.2022.729",

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T1 - THE ZERO-DIVISOR GRAPHS OF Z(+)Zn AND (Z(+)Zn )[X ]

AU - Park, Min Ji

AU - Jeong, Jong Won

AU - Lim, Jung Wook

AU - Bae, Jin Won

PY - 2022

Y1 - 2022

N2 - 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 zerodivisor 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 zerodivisor graphs of Z(+)Zn and (Z(+)Zn)[X]].

AB - 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 zerodivisor 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 zerodivisor graphs of Z(+)Zn and (Z(+)Zn)[X]].

KW - chromatic number

KW - clique

KW - diameter

KW - girth

KW - Γ((Z(+)Z)[X]])

KW - Γ(Z(+)Z)

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JF - Journal of Applied Mathematics and Informatics

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ER -

THE ZERO-DIVISOR GRAPHS OF Z(+)Z_n AND (Z(+)Z_n )[X ]

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Keywords

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