The zero-divisor graph of the ring of integers modulo n

Seung Jun Pi; Se Hun Kim; Jung Wook Lim

doi:10.5666/KMJ.2019.59.4.591

The zero-divisor graph of the ring of integers modulo n

Seung Jun Pi
, Se Hun Kim
, Jung Wook Lim

Kyungpook National University
Seoul National University

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

4 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	591-601
Number of pages	11
Journal	Kyungpook Mathematical Journal
Volume	59
Issue number	4
DOIs	https://doi.org/10.5666/KMJ.2019.59.4.591
State	Published - 2019

Keywords

Chromatic number
Clique
Diameter
Girth
Ring of integers modulo n
Zero-divisor graph

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10.5666/KMJ.2019.59.4.591

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title = "The zero-divisor graph of the ring of integers modulo n",

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

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T1 - The zero-divisor graph of the ring of integers modulo n

AU - Pi, Seung Jun

AU - Kim, Se Hun

AU - Lim, Jung Wook

N1 - Publisher Copyright: © Kyungpook Mathematical Journal.

PY - 2019

Y1 - 2019

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

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

KW - Chromatic number

KW - Clique

KW - Diameter

KW - Girth

KW - Ring of integers modulo n

KW - Zero-divisor graph

UR - https://www.scopus.com/pages/publications/85085954954

U2 - 10.5666/KMJ.2019.59.4.591

DO - 10.5666/KMJ.2019.59.4.591

M3 - Article

AN - SCOPUS:85085954954

SN - 1225-6951

VL - 59

SP - 591

EP - 601

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

IS - 4

ER -

The zero-divisor graph of the ring of integers modulo n

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Keywords

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