Remarks on the zero-divisor graph of a commutative ring
Tian Yanzhao, Wei Qijiao
TL;DR
This paper investigates the zero-divisor graph of the ring Zn, correcting previous errors and providing formulas and methods to accurately compute its clique number, thereby advancing understanding of its graph-theoretic properties.
Contribution
The paper offers corrected formulas and a new construction method for calculating the clique number of the zero-divisor graph G(Zn).
Findings
Corrected previous errors in clique number calculations.
Provided explicit formulas for the clique number of G(Zn).
Introduced a new method to compute the clique number.
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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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models