Remarks on the zero-divisor graph of a commutative ring

Tian Yanzhao; Wei Qijiao

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arXiv · 1501.05704

Remarks on the zero-divisor graph of a commutative ring

Tian Yanzhao·Wei Qijiao

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Abstract

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.

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Tian Yanzhao, Wei Qijiao. 2015-02-02. Remarks on the zero-divisor graph of a commutative ring. https://arxiv.org/abs/1501.05704

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