Remarks on the zero-divisor graph of a commutative ring

Remarks on the zero-divisor graph of a commutative ring

In 1988, I.Beck showed that the chromatic number of G(Zn) is equal to its clique number.In 2004, S.Akbari and A.Mohammadian proved that the edge chromatic number of G(Zn) is equal to its maximum degree,in 2008, J.Skowronek-kaziow give formulas calculating the clique number and the maximum degree of...

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Bibliographic Details
Main Authors: Yanzhao, Tian, Qijiao, Wei
Format: Journal Article
Language:English
Published: 22-01-2015
Subjects:
Mathematics - Commutative Algebra
Mathematics - Number Theory
Online Access:Get full text
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Summary:In 1988, I.Beck showed that the chromatic number of G(Zn) is equal to its clique number.In 2004, S.Akbari and A.Mohammadian proved that the edge chromatic number of G(Zn) is equal to its maximum degree,in 2008, J.Skowronek-kaziow give formulas calculating the clique number and the maximum degree of G(Zn), but he have a error about clique number of G(Zn), we consider the zero-divisor graph G(Zn) of the ring Zn.we give formulas calculating the clique number of G(Zn).We present a constructed method to calculate the clique number.
DOI:10.48550/arxiv.1501.05704